Abstract
It is shown, using results of Koshevnik and Levit (1976), that the average derivative estimator of Haerdle and Stoker (1989) is the asymptotically efficient nonparametric estimator of the average derivative of regression function.
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References
Begun, J., W. Hall, Huang W.-M., and Wellner J. (1983) “Information and Asymptotic Efficiency in Parametric-Nonparametric Models”, The Annals of Statistics, 11, 432–452.
Hájek, J. (1972) “Local Asymptotic Minimax and Admissibility in Estimation”, Proceedings of the Sixth Berkeley Symposium, I, 175–194.
Haerdle, W. and Stoker T. (1989) “Investigating Smooth Multiple Regression by the Method of Average Derivatives”, Journal of the American Statistical Association, vol. 84, 986–995.
Ibragimov, I. and Has’minsky R. (1981), Statistical Estimation: Asymptotic Theory, Springer Verlag, New York.
Ichimura, H. (1988), “Estimation of Single Index Models”, Ph.D. dissertation, Dept. of Economics, MIT.
Koshevnik, Ya. and Levit B. (1976) “On a Nonparametric Analogue of Information Matrix”, Theory of Probability and its Applications, 21, 738–753.
Levit, B. (1978) “Asymptotically Efficient Estimation of Nonlinear Functionals”, Problems of Information Transmission, 14, 204–209.
Newey, W. and Stoker T. (1988) “Efficiency Properties of Average Derivative Estimators”, paper presented at the summer meeting of the American Econometric Society, Minneapolis, June 1988.
Powell, J., Stock J., and Stoker T. (1989) “Semiparametric Estimation of Index Coefficients”, Econometrica, 57, 637–648.
Samarov, A. (1990) “Exploring Regression Structure Using Nonparametric Functional Estimation”, unpublished manuscript.
Stoker, T. (1986) “Consistent Estimation of Scaled Coefficients”, Econometrica, 54, 1461–1481.
Stoker, T. (1987) “Equivalence of Direct and Indirect Estimatorsof Average Derivatives”, WR# 1961–87, Sloan School of Management, MIT, November 1987.
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© 1991 Springer Science+Business Media Dordrecht
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Samarov, A. (1991). On Asymptotic Efficiency of Average Derivative Estimates. In: Roussas, G. (eds) Nonparametric Functional Estimation and Related Topics. NATO ASI Series, vol 335. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3222-0_12
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DOI: https://doi.org/10.1007/978-94-011-3222-0_12
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