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7 - Functions: Interpolation, Smoothing, and Approximation

Published online by Cambridge University Press:  01 June 2011

John F. Monahan
Affiliation:
North Carolina State University
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Publisher: Cambridge University Press
Print publication year: 2011

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References

Abramowitz, Milton and Stegun, Irene A. (Eds.) (1970), Handbook of Mathematical Functions. New York: Dover.Google Scholar
Ahlberg, J. H., Nilsson, E. N., and Walsh, J. L. (1967), The Theory of Splines and Their Applications. New York: Academic Press.Google Scholar
Bailey, B. J. R. (1981), “Alternatives to Hastings' Approximation to the Inverse of the Normal Cumulative Distribution Function,” Applied Statistics 30: 275–6.CrossRefGoogle Scholar
Bates, Douglas M., Lindstrom, Mary J., Wahba, Grace, and Yandell, Brian S. (1987), “GCVPACK: Routines for Generalized Cross Validation,” Communications in Statistics B 16: 263–97.CrossRefGoogle Scholar
Bloomfield, Peter (1976), Fourier Analysis of Time Series: An Introduction. New York: Wiley.Google Scholar
Bosten, N. E. and Battiste, E. L. (1973), “Remark on Algorithm 179, Incomplete Beta Ratio,” Communications of the ACM 17: 156–7.Google Scholar
Cody, W. J., Fraser, W., and Hart, J. F. (1968), “Rational Chebyshev Approximation Using Linear Equations,” Numerische Mathematik 12: 242–51.CrossRefGoogle Scholar
Cody, William J. and Waite, William (1980), Software Manual for the Elementary Functions. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Craven, P. and Wahba, G. (1979), “Smoothing Noisy Data with Spline Functions,” Numerische Mathematik 31: 377–403.CrossRefGoogle Scholar
Dahlquist, Germund and Bjorck, Ake (1974), Numerical Methods (trans. by Anderson, N.). Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Davis, Philip J. (1975), Interpolation and Approximation. New York: Dover.Google Scholar
Boor, Carl De (1978), A Practical Guide to Splines. New York: Springer-Verlag.CrossRefGoogle Scholar
DiDonato, Armido R. and Morris, Alfred H. Jr., (1992), “Algorithm 708: Significant Digit Computation of the Incomplete Beta Ratio,” ACM Transactions on Mathematical Software 18: 360–73.CrossRefGoogle Scholar
Divgi, D. R. (1979), “Calculation of Univariate and Bivariate Normal Probability Functions,” Annals of Statistics 7: 903–10.CrossRefGoogle Scholar
Dresner, Zvi (1978), “Computation of the Bivariate Normal Integral,” Mathematics of Computation 32: 277–9.CrossRefGoogle Scholar
Dresner, Zvi and Wesolowsky, G. O. (1990), “On the Computation of the Bivariate Normal Integral,” Journal of Statistical Computation and Simulation 35: 101–7.CrossRefGoogle Scholar
Eppright, E. S., Fox, H. M., Fryer, B. A., Lamkin, G. H., Vivian, V. M., and Fuller, E. S. (1972), “Nutrition of Infants and Preschool Children in the North Central Region of the United States of America,” World Review of Nutrition and Dietetics 14: 269–332.CrossRefGoogle ScholarPubMed
Eubank, R. L. (1988), Spline Smoothing and Nonparametric Regression. New York: Marcel Dekker.Google Scholar
Fike, C. T. (1968), Computer Evaluation of Mathematical Functions. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Fuller, Wayne A. (1996), Introduction to Statistical Time Series, 2nd ed. New York: Wiley.Google Scholar
Gautschi, W. (1979), “A Computational Procedure for Incomplete Gamma Functions,” ACM Transactions on Mathematical Software 5: 466–81.CrossRefGoogle Scholar
Hall, C. A. and Meyer, W. W. (1976), “Optimal Error Bounds for Cubic Spline Interpolation,” Journal of Approximation Theory 16: 105–22.CrossRefGoogle Scholar
Hart, John F., Cheney, E. W., Lawson, Charles L., Maehly, Hans J., Mesztenyi, Charles K., Rice, John R., Thatcher, Henry G. Jr., and Witzgall, Christoph (1968), Computer Approximations. New York: Wiley; reprinted 1978 by Kreiger (Malabar, FL).Google Scholar
Hastings, C. (1955), Approximations for Digital Computers. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Hutchinson, M. F. (1986), “Algorithm 642: A Fast Procedure for Calculating Minimum Cross-Validation Cubic Smoothing Splines,” ACM Transactions on Mathematical Software 12: 150–3.CrossRefGoogle Scholar
Lew, Robert A. (1981), “An Approximation to the Cumulative Normal Distribution with Simple Coefficients,” Applied Statistics 30: 299–301.CrossRefGoogle Scholar
Ling, Robert F. (1978), “A Study of the Accuracy of Some Approximation for t, chi-square, and F Tail Probabilities,” Journal of the American Statistical Association 73: 274–83.Google Scholar
Majumder, K. L. and Bhattacharjee, G. P. (1973), “Algorithm AS63: The Incomplete Beta Integral,” Applied Statistics 22: 409–11.CrossRefGoogle Scholar
Monahan, John F. (1981), “Approximating the Log of the Normal Cumulative,” in Eddy, W. F. (Ed.), Computer Science and Statistics: Proceedings of the Thirteenth Annual Symposium on the Interface, pp. 304–7. New York: Springer-Verlag.Google Scholar
Monahan, John F. and Stefanski, Leonard A. (1992), “Normal Scale Mixture Approximations to F(z) and Computation of the Logistic–Normal Integral,” in Balakrishnan, N. (Ed.), Handbook of the Logistic Distribution, pp. 529–40. New York: Marcel Dekker.Google Scholar
Odeh, R. E. and Evans, J. O. (1974), “Algorithm AS70: The Percentile Points of the Normal Distribution,” Applied Statistics 23: 96–7.CrossRefGoogle Scholar
Poirier, Dale J. (1973), “Piecewise Regression Using Cubic Splines,” Journal of the American Statistical Association 68: 515–24.Google Scholar
Reinsch, Christian H. (1967), “Smoothing by Spline Functions,” Numerische Mathematik 10: 177–83.CrossRefGoogle Scholar
Reinsch, Christian H. (1971), “Smoothing by Spline Functions II,” Numerische Mathematik 16: 451–4.CrossRefGoogle Scholar
Ruben, Harold (1961), “Probability Contents of Regions under Spherical Normal Distributions III: The Bivariate Normal Integral,” Annals of Mathematical Statistics 32: 171–86.CrossRefGoogle Scholar
Ruppert, David, Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression. New York: Cambridge University Press.CrossRefGoogle Scholar
Silverman, B. W. (1985), “Some Aspects of the Spline Smoothing Approach to Nonparametric Regression Curve Fitting,” Journal of the Royal Statistical Society B 47: 1–52.Google Scholar
Soper, H. E. (1921), “The Numerical Evaluation of the Incomplete Beta-Function,” in Tracts for Computers (no. 7). Cambridge University Press.Google Scholar
Szego, G. (1959), Orthogonal Polynomials. Providence, RI: American Mathematical Society.Google Scholar
Vedder, John D. (1993), “An Invertible Approximation to the Normal Distribution Function,” Computational Statistics and Data Analysis 16: 119–23.CrossRefGoogle Scholar

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