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References

Published online by Cambridge University Press:  03 February 2022

Timothy DelSole
Affiliation:
George Mason University, Virginia
Michael Tippett
Affiliation:
Columbia University, New York
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References

Agresti, A. 2012. Categorical Data Analysis. Wiley.Google Scholar
Akaike, H. 1973. Information Theory and an Extension of the Maximum Likelihood Principle. Pages 267281 of: Petrov, B. N., and Czáki, F. (eds.), 2nd International Symposium on Information Theory. Akademiai Kiadó.Google Scholar
Allen, M. R., and Stott, P. A. 2003. Estimating Signal Amplitudes in Optimal Fingerprinting, Part I: Theory. Clim. Dyn., 21, 477491.Google Scholar
Allen, M. R., and Tett, S. F. B. 1999. Checking for Model Consistency in Optimal Fingerprinting. Clim. Dyn., 15, 419434.Google Scholar
Anderson, E., Bai, Z., Bishof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenny, A., Ostouchov, S., and Sorensen, D. 1992. LAPACK User’s Guide. Philadelphia, PA: Society for Industrial and Applied Mathematics. 235pp.Google Scholar
Anderson, J. L. 2001. An Ensemble Adjustment Filter for Data Assimilation. Mon. Wea. Rev., 129, 28842903.2.0.CO;2>CrossRefGoogle Scholar
Anderson, J. L. 2007. An Adaptive Covariance Inflation Error Correction Algorithm for Ensemble Filters. Tellus, 59A, 210224.CrossRefGoogle Scholar
Anderson, T. W. 1984. An Introduction to Multivariate Statistical Analysis. Wiley-Interscience.Google Scholar
Archer, D. 2010. The Global Carbon Cycle. Princeton University Press.Google Scholar
Baker, M. 2016. Is There a Reproducibility Crisis? Nature, 533, 452454.Google Scholar
Bartlett, M. S. 1937. Properties of Sufficiency and Statistical Tests. Proceedings of the Royal Society of London. Series A – Mathematical and Physical Sciences, 160(901), 268–282.Google Scholar
Bartlett, M. S. 1946. On the Theoretical Specification and Sampling Properties of Autocor-related Time-Series. Supplement to the Journal of the Royal Statistical Society, 8(1), 2741.Google Scholar
Battisti, D. S., and Sarachik, E. S. 1995. Understanding and Predicting ENSO. Rev. Geophys., 33(S2), 13671376.Google Scholar
Bender, Ralf, and Lange, Stefan. 2001. Adjusting for multiple testing: When and How? J. Clin. Epid., 54(4), 343349.Google Scholar
Benjamini, Y., and Hochberg, Y. 1995. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society. Series B (Methodological), 57(1), 289300.Google Scholar
Berger, J. O. 1985. Statistical Decision Theory and Bayesian Analysis. 2nd ed. Springer.Google Scholar
Bernstein, D. S. 2009. Matrix Mathematics: Theory, Facts, and Formulas. Princeton University Press.CrossRefGoogle Scholar
Bierman, G. J. 1977. Factorization Methods for Discrete Sequential Estimation. Mathematics in Science and Engineering. Academic Press. 241 pp.Google Scholar
Bishop, Craig H., Etherton, Brian, and Majumdar, Sharanya J. 2001. Adaptive Sampling with the Ensemble Transform Kalman Filter. Part I: Theoretical Aspects. Mon. Wea. Rev., 129, 420436.Google Scholar
Bode, H. W., and Shannon, C. E. 1950. A Simplified Derivation of Least Squares Smoothing and Prediction Theory. Proc. IRE, 38, 417425.Google Scholar
Box, G. E. P. 1953. Non-Normality and Tests on Variances. Biometrika, 40(3/4), 318335.Google Scholar
Box, George E. P., and Watson, G. S. 1962. Robustness to Non-normality of Regression Tests. Biometrika, 49, 93106.Google Scholar
Box, George E. P., Jenkins, Gwilym M., and Reinsel, Gregory C. 2008. Time Series Analysis: Forecasting and Control. 4th ed. Wiley-Interscience.CrossRefGoogle Scholar
Bretherton, Christopher S., Widmann, Martin, Dymnikov, Valentin P., Wallace, John M., and Bladé, Ileana. 1999. The Effective Number of Spatial Degrees of Freedom of a Time-Varying Field. J. Climate, 12(7), 19902009.2.0.CO;2>CrossRefGoogle Scholar
Brockwell, P. J., and Davis, R. A. 1991. Time Series: Theory and Methods. 2nd ed. Springer Verlag.Google Scholar
Broomhead, D. S., and King, G. P. 1986. Extracting Qualitative Dynamics from Experimental Data. Physica D, 20, 217236.Google Scholar
Burgers, Gerrit, van Leeuwen, Peter Jan, and Evensen, Geir. 1998. Analysis Scheme in the Ensemble Kalman Filter. Mon. Wea. Rev., 126, 17191724.Google Scholar
Burnham, K. P., and Anderson, D. R. 2002. Model Selection and Multimodel Inference: A Practical Information-theoretic Approach. 2nd ed. Springer.Google Scholar
Cane, Mark A., Zebiak, Stephen E., and Dolan, Sean C. 1986. Experimental Forecasts of El Niño. Nature, 321(6073), 827832.Google Scholar
Cane, Mark A., Clement, Amy C., Murphy, Lisa N., and Bellomo, Katinka. 2017. Low-Pass Filtering, Heat Flux, and Atlantic Multidecadal Variability. J. Climate, 30(18), 75297553.Google Scholar
Chin, Edwin H. 1977. Modeling Daily Precipitation Occurrence Process with Markov Chain. Water Resources Research, 13(6), 949956.Google Scholar
Cohen, Jonathan P. 1982. Convergence Rates for the Ultimate and Pentultimate Approximations in Extreme-Value Theory. Advances in Applied Probability, 14(4), 833854.Google Scholar
Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values. Springer.Google Scholar
Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. Wiley-Interscience.Google Scholar
Cover, T. M., and Thomas, J. A. 1991. Elements of Information Theory. Wiley-Interscience.Google Scholar
Cressie, N., and Wikle, C. K. 2011. Statistics for Spatio-Temporal Data. Wiley.Google Scholar
Cryer, J. D., and Chan, K.-S. 2010. Time Series Analysis with Applications in R. Springer.Google Scholar
Davison, A., Huser, R., and Thibaud, E. 2019. Handbook of Environmental and Ecological Statistics. CRC Press.Google Scholar
Dee, Dick P. 1995. On-line Estimation of error Covariance Parameters for Atmospheric Data Assimilation. Mon. Wea. Rev., 123, 11281145.2.0.CO;2>CrossRefGoogle Scholar
Dee, Dick P., and da Silva, Arlindo M. 1998. Data Assimilation in the Presence of Forecast Bias. Quart. J. Roy. Meteor. Soc., 124, 269297.Google Scholar
DelSole, T. 2004. Predictability and Information Theory Part I: Measures of Predictability. J. Atmos. Sci., 61, 24252440.Google Scholar
DelSole, T. 2011. State and Parameter Estimation in Stochastic Dynamical Models. ECMWF Proceedings on Representing Model Uncertainty and Error in Numerical Weather and Climate Prediction Models, 255–262.Google Scholar
DelSole, T., and Chang, P. 2003. Predictable Component Analysis, Canonical Correlation Analysis, and Autoregressive Models. J. Atmos. Sci., 60, 409416.Google Scholar
DelSole, T., and Shukla, J. 2009. Artificial Skill Due to Predictor Screening. J. Climate, 22, 331345.Google Scholar
DelSole, T., and Tippett, M. K. 2009. Average Predictability Time: Part II: Seamless Diagnosis of Predictability on Multiple Time Scales. J. Atmos. Sci., 66, 11881204.Google Scholar
DelSole, T., and Tippett, M. K. 2014. Comparing Forecast Skill. Mon. Wea. Rev., 142, 46584678.Google Scholar
DelSole, T., and Tippett, M. K. 2017. Predictability in a Changing Climate. Clim. Dyn., Oct.Google Scholar
DelSole, T., and Tippett, M. K. 2020. Comparing Climate Time Series – Part 1: Univariate Test. Adv. Stat. Clim. Meteorol. Oceanogr., 6(2), 159175.Google Scholar
DelSole, T. and Tippett, M. K. 2021a. A Mutual Information Criterion with applications to Canonical Correlation Analysis and graphical models. Stat, 10(1):e385.Google Scholar
DelSole, T., and Tippett, M. K. 2021b. Correcting the Corrected AIC. Statistics & Probability Letters, 109064.Google Scholar
DelSole, T., and Yang, X. 2011. Field Significance of Regression Patterns. J. Climate, 24, 50945107.Google Scholar
DelSole, T., Trenary, L., Yan, X., and Tippett, Michael K. 2018. Confidence Intervals in Optimal Fingerprinting. Clim. Dyn., Jul.Google Scholar
dePillis, J. 2002. 777 Mathematical Conversation Starters. America Mathematical Society.Google Scholar
Déqué, M. 1988. 10-day Predictability of the Northern Hemisphere Winter 500-mb Height by the ECMWF Operational Model. Tellus, 40A, 2636.Google Scholar
Déqué, M., Royer, J. F., Stroe, R., and France, Meteo. 1994. Formulation of Gaussian Probability Forecasts Based on Model Extended-range Integrations. Tellus A, 46(1), 5265.Google Scholar
Dommenget, Dietmar, and Latif, Mojib. 2002. A Cautionary Note on the Interpretation of EOFs. J. Climate, 15(2), 216225.Google Scholar
Efron, B., and Tibshirani, R. J. 1994. An Introduction to the Bootstrap. Chapman & Hall.Google Scholar
Efthimiou, C. 2011. Introduction to Functional Equations: Theory and Problem-solving Strategies for Mathematical Competitions and Beyond (MSRI Mathematical Circles Library). American Mathematical Society.Google Scholar
Evensen, G. 1994. Sequential Data Assimilation with a Nonlinear Quasi-geostrophic Model using Monte Carlo Methods to Forecast Error Statistics. J. Geophys. Res., 99, 10431062.Google Scholar
Fan, Yun, and van den Dool, Huug. 2008. A Global Monthly Land Surface Air Temperature Analysis for 1948–present. Journal of Geophysical Research: Atmospheres, 113(D1).Google Scholar
Farrell, Brian F., and Ioannou, Petros J. 1996. Generalized Stability Theory. Part I: Autonomous Operators. J. Atmos. Sci., 53, 20252040.Google Scholar
Farrell, Brian F., and Ioannou, Petros J. 2001. Accurate Low-Dimensional Approximation of the Linear Dynamics of Fuid Flow. J. Atmos. Sci., 58(18), 27712789.Google Scholar
Feynman, R. P., Leighton, R. B., and Sands, M. 1977. The Feynman Lectures on Physics, Vol. 1: Mainly Mechanics, Radiation, and Heat. Addison-Wesley.Google Scholar
Fisher, R. A. 1915. Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population. Biometrika, 10(4), 507521.Google Scholar
Fisher, R. A. 1921. On the ‘Probable Error’ of a Coefficient of Correlation Deduced from a Small Sample. Metron, 1, 132.Google Scholar
Fisher, R. A. 1936. Has Mendel’s Work Been Rediscovered? Annals of Science, 1(2), 115137.Google Scholar
Fisher, R. A., and Tippett, L. H. C. 1928. Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample. Mathematical Proceedings of the Cambridge Philosophical Society, 24(4), 180190.Google Scholar
Flury, B. N. 1985. Analysis of Linear Combinations with Extreme Ratios of Variance. J. Amer. Stat. Assoc., 80, 915922.Google Scholar
Fujikoshi, Y. 1985. Selection of Variables in Discriminant Analysis and Canonical Correlation Analysis. Pages 219236 of: Krishnaiah, P. R. (ed), Multivariate Analysis VI: Proceedings of the Sixth International Symposium on Multivariate Analysis. Elsevier.Google Scholar
Fujikoshi, Y., Ulyanov, V. V., and Shimizu, R. 2010. Multivariate Statistics: High-dimensional and Large-Sample Approximations. John Wiley and Sons.Google Scholar
Gaspari, Gregory, and Cohn, Stephen E. 1999. Construction of Correlation Functions in Two and Three Dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757.Google Scholar
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. 2004. Bayesian Data Analysis. 2nd ed. Chapman and Hall.Google Scholar
Ghil, M., Allen, M. R., Dettinger, M. D., Ide, K., Kondrashov, D., Mann, M. E., Robertson, A. W., Saunders, A., Tian, Y., Varadi, F., and Yiou, P. 2002. Advanced Spectral Methods for Climatic Time Series. Rev. Geophys., 40, 3.1–3.41.Google Scholar
Gilleland, E., and Katz, R. 2016. extRemes 2.0: An Extreme Value Analysis Package in R. J. Stat. Software, 72(1), 139.Google Scholar
Glantz, S. A, and Slinker, B. K. 2016. Primer of Applied Regression and Analysis of Variance. 3rd ed. McGraw-Hill.Google Scholar
Gneiting, T., and Raftery, A. E. 2007. Strictly Proper Scoring Rules, Prediction, and Estimation. J. Am. Stat. Assoc., 102, 359378.Google Scholar
Golub, Gene H., and Van Loan, Charles F. 1996. Matrix Computations. Third ed. Baltimore: The Johns Hopkins University Press. 694 pp. Good, P. I. 2005. Permutation, Parametric and Bootstrap Tests of Hypotheses. 3rd ed. Springer.Google Scholar
Good, P. I. 2006. Resampling Methods. 3rd ed. Birkhäuser.Google Scholar
Hamill, Thomas M., Whitaker, Jeffrey S., and Snyder, Chris. 2001. Distance-Dependent Filtering of Background Error Covariance Estimates in an Ensemble Kalman Filter. Mon. Wea. Rev., 129, 27762790.Google Scholar
Hamill, Thomas M., Bates, Gary T., Whitaker, Jeffrey S., Murray, Donald R., Fiorino, Michael, Galarneau, Thomas J., Zhu, Yuejian, and Lapenta, William. 2013. NOAA’s Second-Generation Global Medium-Range Ensemble Reforecast Dataset. Bull. Amer. Meteor. Soc., 94(10), 15531565.Google Scholar
Hannan, E. J., and Quinn, B. G. 1979. The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society. Series B (Methodological), 41(2), 190195.Google Scholar
Hansen, James, and Lebedeff, Sergej. 1987. Global Trends of Measured Surface Air Temperature. J. Geophys. Research: Atmospheres, 92(D11), 1334513372.Google Scholar
Hansen, M. H., and Yu, B. 2001. Model Selection and the Principle of Minimum Description Length. J. Amer. Stat. Assoc., 96, 746774.Google Scholar
Harrell, F. 2001. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. Springer.Google Scholar
Harvey, A. C. 1989. Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press.Google Scholar
Harville, D. A. 1997. Matrix Algebra from a Statistician’s Perspective. Springer.Google Scholar
Hasselmann, K. 1976. Stochastic Climate Models I. Theory. Tellus, 28, 473485.Google Scholar
Hastie, T., Tibshirani, R., and Friedman, J. H. 2009. Elements of Statistical Learning. 2nd ed. Springer.Google Scholar
Hays, J. D., Imbrie, John, and Shackleton, N. J. 1976. Variations in the Earth’s Orbit: Pacemaker of the Ice Ages. Science, 194(4270), 11211132.Google Scholar
Henderson, Douglas A., and Denison, Daniel R. 1989. Stepwise Regression in Social and Psychological Research. Psychological Reports, 64(1), 251257.Google Scholar
Hodges, J. L., and Lehmann, E. L. 1956. The Efficiency of Some Nonparametric Competitors of the t-Test. The Annals of Mathematical Statistics, 27(2), 324335.Google Scholar
Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. 1999. Bayesian Model Averaging: A Tutorial. Statist. Sci., 14, 382417.Google Scholar
Horn, R. A., and Johnson, C. R. 1985. Matrix Analysis. New York: Cambridge University Press. 561 pp.Google Scholar
Hosking, J. R. M., Wallis, J. R., and Wood, E. F. 1985. Estimation of the Generalized Extreme-Value Distribution by the Method of Probability-Weighted Moments. Technometrics, 27(3), 251261.Google Scholar
Hotelling, H. 1933. Analysis of a Complex of Statistical Variables into Principal Components. J. Educational Psychology, 24, 417441.Google Scholar
Hotelling, Harold. 1936. Relations between Two Sets of Variates. Biometrika, 28(3/4), 321377.Google Scholar
Houtekamer, P. L., and Mitchell, Herschel L. 1998. Data Assimilation Using an Ensemble Kalman Filter Technique. Mon. Wea. Rev., 126, 796811.Google Scholar
Houtekamer, P. L., and Mitchell, Herschel L. 2001. A Sequential Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev., 129, 123137.Google Scholar
Houtekamer, P. L., and Mitchell, Herschel L. 2005. Ensemble Kalman Filtering. Quarterly J. Roy. Met. Soc., 131(613), 32693289.Google Scholar
Houtekamer, P. L., and Zhang, Fuqing. 2016. Review of the Ensemble Kalman Filter for Atmospheric Data Assimilation. Mon. Wea. Rev., 144(12), 44894532.Google Scholar
Huang, Boyin, Banzon, Viva F., Freeman, Eric, Lawrimore, Jay, Liu, Wei, Peterson, Thomas C., Smith, Thomas M., Thorne, Peter W., Woodruff, Scott D., and Zhang, Huai-Min. 2015. Extended Reconstructed Sea Surface Temperature Version 4 (ERSST.v4). Part I: Upgrades and Intercomparisons. J. Climate, 28(3), 911930.Google Scholar
Huang, Boyin, Thorne, Peter W., Banzon, Viva F., Boyer, Tim, Chepurin, Gennady, Lawrimore, Jay H., Menne, Matthew J., Smith, Thomas M., Vose, Russell S., and Zhang, Huai-Min. 2017. Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5): Upgrades, Validations, and Intercomparisons. J. Climate, 30(20), 81798205.Google Scholar
Hurvich, C. M., and Tsai, C.-L. 1989. Regression and Time Series Model Selection in Small Samples. Biometrika, 76(2), 297307.Google Scholar
Hyndman, Rob J., and Fan, Yanan. 1996. Sample Quantiles in Statistical Packages. The American Statistician, 50(4), 361365.Google Scholar
International Committee of Medical Journal Editors. 2019. Recommendations for the Conduct, Reporting, Editing, and Publication of Scholarly Work in Medical Journals.Google Scholar
Ioannidis, J. P. A. 2005. Why Most Published Research Findings Are False. PLOSMed, 2, 696701.Google Scholar
Jazwinski, A. H. 1970. Stochastic Processes and Filtering Theory. New York: Academic Press. 376 pp.Google Scholar
Jenkins, G. M, and Watts, D. G. 1968. Spectral Analysis and Its Applications. Holden-Day.Google Scholar
Johnson, R. A., and Bhattacharyya, G. K. 1992. Statistics: Principles and Methods. 2nd ed. John Wiley and Sons.Google Scholar
Johnson, R. A., and Wichern, D. W. 2002. Applied Multivariate Statistical Analysis. 5th ed. Prentice-Hall.Google Scholar
Jolliffe, I. T. 2002. Principal Component Analysis. Springer.Google Scholar
Jolliffe, Ian T. 2003. A Cautionary Note on Artificial Examples of EOFs. J. Climate, 16(7), 10841086.Google Scholar
Jones, P. D., Osborn, T. J., and Briffa, K. R. 1997. Estimating Sampling Errors in Large-Scale Temperature Averages. J. Climate, 10(10), 25482568.Google Scholar
Kalman, R.E. 1960. A New Approach to Linear Filtering and Prediction Problems. Trans. ASME, Ser. D, J. Basic Eng., 82, 3545.Google Scholar
Katz, Richard W. 1977. Precipitation as a Chain-dependent Process. J. Appl. Meteor., 16, 671676.Google Scholar
Kendall, M. G. 1946. Contributions to the Study of Oscillatory Time-Series.Google Scholar
Kirchmeier-Young, Megan C., Zwiers, Francis W., and Gillett, Nathan P. 2016. Attribution of Extreme Events in Arctic Sea Ice Extent. J. Climate, 30(2), 553571.Google Scholar
Kolmogorov, A. 1992. 15. On The Empirical Determination of a Distribution Law. Pages 139–146 of: Shiryayev, A. N. (ed.), Selected Works of A. N. Kolmogorov: Volume II Probability Theory and Mathematical Statistics. Springer Netherlands.Google Scholar
Kotz, S., and Nadarajah, S. 2000. Extreme Value Distributions: Theory and Applications. Imperial College Press.Google Scholar
Krüger, T. 2013. Discovering the Ice Ages: International Reception and Consequences for a Historical Understanding of Climate. Brill.Google Scholar
LaJoie, E., and DelSole, T. 2016. Changes in Internal Variability Due to Anthropogenic Forcing: A New Field Significance Test. J. Climate, 29(15), 55475560.Google Scholar
Lauritzen, S. L. 1981. Time Series Analysis in 1880: A Discussion of Contributions Made by T. N. Thiele. Int. Statist. Rev., 49, 319331.Google Scholar
Lawley, D. N. 1956. Tests of Significance for the Latent Roots of Covariance and Correlation Matrices. Biometrika, 43, 128136.Google Scholar
Lehman, E. L., and Romano, J. P. 2005. Testing Statistical Hypotheses. Springer.Google Scholar
Leith, C. E. 1978. Predictability of climate. Nature, 276(5686), 352–355. Leung, Lai-Yung, and North, Gerald R. 1990. Information Theory and Climate Prediction. J. Climate, 3, 514.Google Scholar
Livezey, Robert E., and Chen, W.Y. 1983. Statistical Field Significance and Its Determination by Monte Carlo Techniques. Mon Wea. Rev., 111, 4659.Google Scholar
Ljung, G. M., and Box, G. E. P. 1978. On a measure of lack of fit in time series models. Biometrika, 65, 297303.Google Scholar
Lorenc, Andrew C., Bowler, Neill E., Clayton, Adam M., Pring, Stephen R., and Fairbairn, David. 2014. Comparison of Hybrid-4DEnVar and Hybrid-4DVar Data Assimilation Methods for Global NWP. Mon. Wea. Rev., 143(1), 212229.Google Scholar
Lorenz, E. N. 1963. Deterministic Nonperiodic Flow. J. Atmos. Sci., 20, 130141.Google Scholar
Lorenz, E. N. 1969. Three Approaches to Atmospheric Predictability. Bull. Am. Meteor. Soc., 345–351.Google Scholar
Lorenz, E. N., and Emmanuel, K. A. 1998. Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model. J. Atmos. Sci., 55, 399414.Google Scholar
Madden, R. A., and Julian, P. R. 1994. Observations of the 40-50-day Tropical Oscillation-A Review. Mon. Wea. Rev., 122, 814837.Google Scholar
Majda, A., and Tong, X. 2016. Robustness and Accuracy of Finite Ensemble Kalman Filters in Large Dimensions. Comm. Pure Appl. Math, submitted.Google Scholar
Makkonen, Lasse. 2008. Bringing Closure to the Plotting Position Controversy. Communications in Statistics: Theory and Methods, 37(3), 460467.Google Scholar
Mallows, C. L. 1973. Some Comments on CP . Technometrics, 15(4), 661675.Google Scholar
Mann, H. B., and Whitney, D. R. 1947. On a Test of Whether One of Two Random Variables Is Stochastically Larger than the Other. Ann. Math. Statist., 50–60.Google Scholar
Mardia, K. V., Kent, J. T., and Bibby, J. M. 1979. Multivariate Analysis. Academic Press.Google Scholar
Maybeck, P. S. 1982. Stochastic Models, Estimation, and Control. Vol. 1. Academic Press.Google Scholar
McPherson, Ronald D. 1986. Operational Objective Analysis Techniques and Potential Applications for Mesoscale Meteorology. Pages 151172 of: Ray, Peter S. (ed.), Mesoscale Meteorology and Forecasting. American Meteorological Society.Google Scholar
McQuarrie, A. D. R., and Tsai, C.-L. 1998. Regression and Time Series Model Selection. World Scientific Publishing.Google Scholar
Mendenhall, W., Scheaffer, R. L., and Wackerly, D. D. 1986. Mathematical Statistics with Applications. 3rd ed. PWS Publishers.Google Scholar
Miller, A. 2002. Subset Selection in Regression. 2nd ed. Chapman and Hall.Google Scholar
Mood, A. M. 1954. On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests. Ann. Math. Statist., 25(3), 514522.Google Scholar
Morice, Colin P., Kennedy, John J., Rayner, Nick A., and Jones, Phil D. 2012. Quantifying Uncertainties in Global and Regional Temperature Change Using an Ensemble of Observational Estimates: The HadCRUT4 data set. J Geophys. Res.-Atmospheres, 117.Google Scholar
Muirhead, R. J. 2009. Aspects of Multivariate Statistical Theory. John Wiley & Sons.Google Scholar
Mundry, Roger, and Nunn, Charles L. 2009. Stepwise Model Fitting and Statistical Inference: Turning Noise into Signal Pollution. The American Naturalist, 173(1), 119123.Google Scholar
Noble, B., and Daniel, J. W. 1988. Applied Linear Algebra. 3rd ed. Prentice-Hall.Google Scholar
North, Gerald R., Bell, Thomas L., Cahalan, Robert F., and Moeng, Fanthune J. 1982. Sampling Errors in the Estimation of Empirical Orthogonal Functions. Mon. Wea. Rev., 1982, 699706.Google Scholar
Olson, Chester L. 1974. Comparative Robustness of Six Tests in Multivariate Analysis of Variance. J. Am. Stat. Assoc., 69(348), 894908.Google Scholar
Ott, Edward, Hunt, Brian R., Szunyogh, Istvan, Zimin, Aleksey V., Kostelich, Eric J., Corazza, Matteo, Kalnay, Eugenia, Patil, D. J., and Yorke, James A. 2004. A Local Ensemble Kalman Filter for Atmospheric Data Assimilation. Tellus, A56, 415428.Google Scholar
Penland, C., and Sardeshmukh, P. D. 1995. The Optimal-growth of Tropical Sea-surface Temperature Anomalies. J. Climate, 8, 19992024.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Fannerty, B. P. 2007. Numerical Recipes. 3rd ed. Cambridge University Press.Google Scholar
Priestley, M. B. 1981. Spectral Analysis and Time Series. Academic Press.Google Scholar
Rao, C. R. 1973. Linear Statistical Inference and Its Applications. 2nd ed. John Wiley & Sons.Google Scholar
Raymo, M. E., Lisiecki, L. E., and Nisancioglu, Kerim H. 2006. Plio-Pleistocene Ice Volume, Antarctic Climate, and the Global δ 18 O Record. Science, 313(5786), 492495.Google Scholar
Reeves, J., Chen, J., Wang, X. L., Lund, R., and Lu, Q. Q. 2007. A Review and Comparison of Changepoint Detection Techniques for Climate Data. J. Appl. Meteor. Climatol., 46, 900–915.Google Scholar
Rencher, A. C., and Pun, F. C. 1980. Inflation of R2 in Best Subset Regression. Technometrics, 22, 4953.Google Scholar
Rencher, A. C., and Schaalje, G. B. 2008. Linear Models in Statistics. 2nd ed. Wiley-Interscience.Google Scholar
Renwick, James A., and Wallace, John M. 1995. Predictable Anomaly Patterns and the Forecast Skill of Northern Hemisphere Wintertime 500-mb height fields. Mon. Wea. Rev., 123, 21142131.Google Scholar
Ribes, A., Azais, J.-M., and Planton, S. 2009. Adaptation of the Optimal Fingerprint Method for Climate Change Detection Using a Well-conditioned Covariance Matrix Estimate. Climate Dynamics, 33, 707722.Google Scholar
Rosset, Saharon, and Tibshirani, Ryan J. 2020. From Fixed-X to Random-X Regression: Bias-Variance Decompositions, Covariance Penalties, and Prediction Error Estimation. J. Am. Stat. Assoc., 115(529), 138151.Google Scholar
Saha, S., Moorthi, S., Wu, X., Wang, J., Nadiga, S., Tripp, P., Behringer, D., Hou, Y.-T., Chuang, Hui-ya, Iredell, M, ., Ek, M., Meng, J., Yang, R., Mendez, M. P., van den Dool, H., Zhang, Q., Wang, W., Chen, M., and Becker, E. 2014. The NCEP Climate Forecast System Version 2. J. Climate, 27, 21852208.Google Scholar
Sakov, P., and Oke, P. R. 2008. Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters. Mon. Wea. Rev., 136, 10421053.Google Scholar
Scheffé, Henry. 1970. Practical Solutions of the Behrens-Fisher Problem. J. Am. Stat. Assoc., 65(332), 15011508.Google Scholar
Schneider, Tapio, and Griffies, Stephen. 1999. A Conceptual Framework for Predictability Studies. J. Climate, 12, 31333155.Google Scholar
Schneider, Tapio, and Held, Isaac M. 2001. Discriminants of Twentieth-century Changes in Earth Surface Temperatures. J. Climate, 14, 249254.Google Scholar
Shukla, J. 1981. Dynamical Predictability of Monthly Means. Mon. Wea. Rev., 38, 25472572.Google Scholar
Shumway, Robert H., and Stoffer, David S. 2006. Time Series Analysis and Its Applications: with R Examples. 2nd ed. Springer.Google Scholar
Siegert, Stefan, Bellprat, Omar, Ménégoz, Martin, Stephenson, David B., and Doblas-Reyes, Francisco J. 2016. Detecting Improvements in Forecast Correlation Skill: Statistical Testing and Power Analysis. Mon. Wea. Rev., 145(2), 437450.Google Scholar
Simon, D. 2006. Optimal State Estimation. Kalman, H , and Nonlinear Approaches. Wiley-Interscience.Google Scholar
Smith, R. L. 1985. Maximum Likelihood Estimation in a Class of Nonregular Cases. Biometrika, 72(1), 6790.Google Scholar
Spiegel, M. R., Schiller, J., and Srinivasan, R. A. 2000. Schaum’s Outline of Theory and Problems in Probability and Statistics. 2nd ed. McGraw-Hill.Google Scholar
Stigler, S. M. 1986. The History of Statistics. Harvard University Press.Google Scholar
Strang, G. 1988. Linear Algebra and Its Applications. Harcourt Brace Jovanovich.Google Scholar
Strang, G. 2016. Introduction to Linear Algebra. Wellesley-Cambridge Press.Google Scholar
Taylor, Geoffrey I. 1962. Gilbert, Thomas Walker. 1868–1958. Biographical Memoirs of Fellows of the Royal Society, 8, 167174.Google Scholar
Taylor, K. E., Stouffer, R. J., and Meehl, G. A. 2012. An Overview of CMIP5 and the Experimental Design. Bull. Am. Meteor. Soc., 93, 485498.Google Scholar
Thompson, Bruce. 1995. Stepwise Regression and Stepwise Discriminant Analysis Need Not Apply Here: A Guidelines Editorial. Educational and Psychological Measurement, 55(4), 525534.Google Scholar
Tian, S., Hurvich, C. M., and Simonoff, J. S. 2020. Selection of Regression Models under Linear Restrictions for Fixed and Random Designs. ArXiv e-prints, 28.Google Scholar
Tippett, Michael K., Anderson, J. L., Bishop, Craig H., Hamill, Thomas M., and Whitaker, J. S. 2003. Ensemble Square-root Filters. Mon. Wea. Rev., 131, 14851490.Google Scholar
Torrence, C., and Webster, P. J. 1998. The Annual Cycle of Persistence in the El Niño/Southern Oscillation. Quart. J. Roy. Meteor. Soc., 124, 19852004.Google Scholar
Van Huffel, S., and Vandewalle, J. 1991. The Total Least Squares Problem. Society for Industrial and Applied Mathematics.Google Scholar
Ventura, Valérie, Paciorek, Christopher J., and Risbey, James S. 2004. Controlling the Proportion of Falsely Rejected Hypotheses When Conducting Multiple Tests with Climatological Data. J. Climate, 17(22), 43434356.Google Scholar
Venzke, S., Allen, M. R., Sutton, R. T., and Rowell, D. P. 1999. The Atmospheric Response over the North Atlantic to Decadal Changes in Sea Surface Temperature. J. Climate, 12, 25622584.Google Scholar
Vinod, H. D. 1976. Canonical Ridge and Econometrics of Joint Production. Journal of Econometrics, 4(2), 147166.Google Scholar
von Storch, Hans, and Zwiers, Francis W. 1999. Statistical Analysis in Climate Research. Cambridge University Press.Google Scholar
Walker, G. T., and Bliss, E. W. 1932. World Weather V. Mem. Roy. Meteor. Soc., 53–84.Google Scholar
Walker, Gilbert. 1928. World Weather. Quarterly Journal of the Royal Meteorological Society, 54(226), 7987.Google Scholar
Wang, Xuguang, Parrish, David, Kleist, Daryl, and Whitaker, Jeffrey. 2013. GSI 3DVar-Based Ensemble–Variational Hybrid Data Assimilation for NCEP Global Forecast System: Single-Resolution Experiments. Mon. Wea. Rev., 141(11), 40984117.Google Scholar
Weare, Bryan C., and Nasstrom, John S. 1982. Examples of Extended Empirical Orthogonal Function Analyses. Mon. Wea. Rev., 110(6), 481485.Google Scholar
Wheeler, M. C., and Hendon, H. 2004. An All-season Real-time Multivariate MJO Index: Development of an Index for Monitoring and Prediction. Mon. Wea. Rev., 132, 19171932.Google Scholar
Whitaker, Jeffery, and Hamill, Thomas M. 2002. Ensemble Data Assimilation without Perturbed Observations. Mon. Wea. Rev., 130, 19131924.Google Scholar
Whittingham, M. J., Stephens, P. A., Bradbury, R. B., and Freckleton, R. P. 2006. Why Do We Still Use Stepwise Modelling in Ecology and Behaviour? J. Anim. Ecol., 75(5), 11821189.Google Scholar
Wiener, N. 1950. Extrapolation, Interpolation, and Smoothing of Stationary Time Series: With Engineering Applications. MIT Press.Google Scholar
Wilcoxon, Frank. 1945. Individual Comparisons by Ranking Methods. Biometrics Bulletin, 1(6), 8083.Google Scholar
Wilks, D. S. 2006. On “Field Significance” and the False Discovery Rate. J. Appl. Meteor. Climatol., 45(9), 11811189.Google Scholar
Wilks, D. S. 2011. Statistical Methods in the Atmospheric Sciences: An Introduction. 3rd ed. Academic Press.Google Scholar
Wilks, D. S. 2016. “The Stippling Shows Statistically Significant Grid Points”: How Research Results are Routinely Overstated and Overinterpreted, and What to Do about it. Bulletin of the American Meteorological Society, 97(12), 22632273.Google Scholar
Wilks, S. S. 1932. Certain Generalizations in the Analysis of Variance. Biometrika, 24(3–4), 471494.Google Scholar
Wills, Robert C., Schneider, Tapio, Wallace, John M., Battisti, David S., and Hartmann, Dennis L. 2018. Disentangling Global Warming, Multidecadal Variability, and El Niño in Pacific Temperatures. Geophys. Res. Lett., 45(5), 24872496.Google Scholar
Witten, Daniela M., Tibshirani, Robert, and Hastie, Trevor. 2009. A Penalized Matrix Decomposition, with Applications to Sparse Principal Components and Canonical Correlation Analysis. Biostatistics, 10(3), 515534.Google Scholar
Wyrtki, Klaus. 1975. El Niño: The Dynamic Response of the Equatorial Pacific Ocean to Atmospheric Forcing. J. Phys. Oceanogr., 5(4), 572584.Google Scholar
Yang, X., and DelSole, T. 2009. Using the ensemble Kalman Filter to Estimate Multiplicative Model Parameters. Tellus, 61, 601609.CrossRefGoogle Scholar
Yule, G. Udny. 1927. On a Method of Investigating Periodicities in Disturbed Series, with Special Reference to Wolfer’s Sunspot Numbers. Phil. Trans. R. Soc. Lond. A, Containing Papers of a Mathematical or Physical Character, 226, 267298.Google Scholar
Zhang, Xuebin, Alexander, Lisa, Hegerl, Gabriele C., Jones, Philip, Tank, Albert Klein, Peterson, Thomas C., Trewin, Blair, and Zwiers, Francis W. 2011. Indices for Monitoring Changes in Extremes Based on Daily Temperature and Precipitation Data. WIREs Clim. Chan., 2(6), 851870.Google Scholar
Zwiers, W. F. 1996. Interannual Variability and Predictability in an Ensemble of AMIP Climate Simulations Conducted with the CCC GCM2. Clim. Dyn., 12(12), 825847.Google Scholar

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  • References
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.024
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  • References
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.024
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  • References
  • Timothy DelSole, George Mason University, Virginia, Michael Tippett, Columbia University, New York
  • Book: Statistical Methods for Climate Scientists
  • Online publication: 03 February 2022
  • Chapter DOI: https://doi.org/10.1017/9781108659055.024
Available formats
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