Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-25T12:33:48.765Z Has data issue: false hasContentIssue false
  • English
  • Français

SMALL BANDWIDTH ASYMPTOTICS FOR DENSITY-WEIGHTED AVERAGE DERIVATIVES

Published online by Cambridge University Press:  20 August 2013

Matias D. Cattaneo ,
Richard K. Crump  and
Michael Jansson
Matias D. Cattaneo
Affiliation:
University of Michigan
Richard K. Crump
Affiliation:
Federal Reserve Bank of New York
Michael Jansson
Affiliation:
UC Berkeley and CREATES
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes (apparently) novel standard error formulas for the density-weighted average derivative estimator of Powell, Stock, and Stoker (Econometrica 57, 1989). Asymptotic validity of the standard errors developed in this paper does not require the use of higher-order kernels, and the standard errors are “robust” in the sense that they accommodate (but do not require) bandwidths that are smaller than those for which conventional standard errors are valid. Moreover, the results of a Monte Carlo experiment suggest that the finite sample coverage rates of confidence intervals constructed using the standard errors developed in this papercoincide (approximately) with the nominal coverage rates across a nontrivial range of bandwidths.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 1 , February 2014 , pp. 176 - 200
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aradillas-Lopez, A., Honore, B.E., & Powell, J.L. (2007) Pairwise difference estimation with nonparametric control variables. International Economic Review 48, 1119–1158.Google Scholar
Cattaneo, M.D., Crump, R.K., & Jansson, M. (2010) Robust data-driven inference for density-weighted average derivatives. Journal of the American Statistical Association 105, 1070–1083.Google Scholar
de Jong, P. (1987) A central limit theorem for generalized quadratic forms. Probability Theory and Related Fields 75, 261–277.CrossRefGoogle Scholar
Eddy, W.F. (1980) Optimum kernel estimators of the mode. Annals of Statistics 8, 870–882.CrossRefGoogle Scholar
Eubank, R.L. & Wang, S. (1999) A central limit theorem for the sum of generalized linear and quadratic forms. Statistics 33, 85–91.CrossRefGoogle Scholar
Fan, Y. & Linton, O. (2003) Some higher-order theory for a consistent non-parametric model specification test. Journal of Statistical Planning and Inference 109, 125–154.Google Scholar
Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Annals of Mathematical Statistics 19, 293–325.Google Scholar
Hristache, M., Juditsky, A., & Spokoiny, V. (2001) Direct estimation of the index coefficient in a single-index model. Annals of Statistics 29, 595–623.Google Scholar
Ichimura, H. & Linton, O. (2005) Asymptotic expansions for some semi-parametric program evaluation estimators. In Andrews, D.W.K. & Stock, J.H. (eds.), Identification and Inference in Econometric Models: Essays in Honor of Thomas J. Rothenberg, pp. 149–170. Cambridge University Press.CrossRefGoogle Scholar
Jammalamadaka, S.R. & Janson, S. (1986) Limit theorems for a triangular scheme of U-statistics with applications to inter-point distances. Annals of Probability 14, 1347–1358.Google Scholar
Jing, B.-Y. & Wang, Q. (2003) Edgeworth expansion for U-statistics under miminal conditions. Annals of Statistics 31, 1376–1391.Google Scholar
Kiefer, N.M. & Vogelsang, T.J. (2002a) Heteroskedasticity-autocorrelation robust standard errors using the Bartlett kernel without truncation. Econometrica 70, 2093–2095.Google Scholar
Kiefer, N.M. & Vogelsang, T.J. (2002b) Heteroskedasticity-Autocorrelation robust testing using bandwidth equal to sample size. Econometric Theory 18, 1350–1366.Google Scholar
Kiefer, N.M. & Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.Google Scholar
Kiefer, N.M., Vogelsang, T.J., & Bunzel, H. (2000) Simple robust testing of regression hypotheses. Econometrica 68, 695–714.CrossRefGoogle Scholar
Neave, H.R. (1970) An improved formula for the asymptotic variance of spectrum estimates. Annals of Mathematical Statistics 41, 70–77.Google Scholar
Newey, W.K. (1994) The asymptotic variance of semiparametric estimators. Econometrica 62, 1349–1382.Google Scholar
Newey, W.K., Hsieh, F., & Robins, J.M. (2004) Twicing kernels and a small bias property of semiparametric estimators. Econometrica 72, 947–962.Google Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F., & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2111–2245. North Holland.Google Scholar
Newey, W.K. & Stoker, T.M. (1993) Efficiency of weighted average derivative estimators and index models. Econometrica 61, 1199–1223.Google Scholar
Nishiyama, Y. & Robinson, P.M. (2000) Edgeworth expansions for semiparametric averaged derivatives. Econometrica 68, 931–979.Google Scholar
Nishiyama, Y. & Robinson, P.M. (2001) Studentization in edgeworth expansions for estimates of semiparametric index models. In Hsiao, C., Morimune, K., & Powell, J.L. (eds.), Nonlinear Statistical Modeling: Essays in Honor of Takeshi Amemiya, pp. 197–240. Cambridge University Press.Google Scholar
Nishiyama, Y. & Robinson, P.M. (2005) The bootstrap and the Edgeworth correction for semiparametric averaged derivatives. Econometrica 73, 903–948.Google Scholar
Parzen, E. (1962) On estimation of a probability density function and mode. Annals of Mathematical Statistics 33, 1065–1076.Google Scholar
Powell, J.L., Stock, J.H., & Stoker, T.M. (1989) Semiparametric estimation of index coefficients. Econometrica 57, 1403–1430.Google Scholar
Powell, J.L. & Stoker, T.M. (1996) Optimal bandwidth choice for density-weighted averages. Journal of Econometrics 75, 291–316.Google Scholar
Robinson, P.M. (1988) Root-N-Consistent semiparametric regression. Econometrica 56, 931–954.Google Scholar
Robinson, P.M. (1995) The normal approximation for semiparametric averaged derivatives. Econometrica 63, 667–680.Google Scholar
Severini, T.A. & Tripathi, G. (2001) A simplified approach to computing efficiency bounds in semiparametric models. Journal of Econometrics 102, 23–66.CrossRefGoogle Scholar
Stoker, T.M. (1986) Consistent estimation of scaled coefficients. Econometrica 54, 1461–1481.CrossRefGoogle Scholar