Abstract
It is shown that the weighted residual-based estimator of Schick, Zhu, and Du (2017) is efficient in some special cases and can be made to be efficient by adding a stochastic correction term. The efficiency is shown by deriving the efficient influence function and establishing a uniform stochastic expansion with this influence function. The correction term relies on estimators of the score function for the errors and other characteristics of the model.
Similar content being viewed by others
References
J. Forrester, W. Hooper, H. Peng, and A. Schick, “On the Construction of Efficient Estimators in Semiparametric Models”, Statist. and Decis. 21, 109–138 (2003).
H. L. Koul, Weighted Empiricals and Linear Models, in IMS Lecture Notes–Monograph Series (1992), Vol. 21, pp. 1–258.
S. Kiwitt, E. R. Nagel, and N. Neumeyer, “Empirical Likelihood Estimators for the Error Distribution in Nonparametric RegressionModels”, Math. Methods Statist. 17, 241–260 (2008).
U. U. Müller and A. Schick, “Efficiency Transfer for RegressionModels with ResponsesMissing at Random”, Bernoulli 23, 2693–2719 (2017).
U. U. Müller, A. Schick, and W. Wefelmeyer, “Estimating Linear Functionals of the Error Distribution in Nonparametric Regression”, J. Statist. Plann. Inference 119, 75–93 (2004).
U. U. Müller, A. Schick, and W. Wefelmeyer, “Weighted Residual-Based Density Estimators for Nonlinear Autoregressive Models”, Statist. Sinica 15, 177–195 (2005).
U. U. Müller, A. Schick, and W. Wefelmeyer, “Estimating the Error Distribution Function in Semiparametric Regression”, Statist. and Decis. 25, 1–18 (2007).
A. Schick, “On Efficient Estimation in Regression Models”, Ann. Statist. 21, 1486–1521 (1993).
A. Schick, Y. Zhu, and X. Du, Estimation of the Error Distribution Function in a Varying Coefficient Regression Model Preprint (2017).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Schick, A., Zhu, Y. Efficient estimation of the error distribution in a varying coefficient regression model. Math. Meth. Stat. 26, 176–195 (2017). https://doi.org/10.3103/S1066530717030024
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066530717030024
Keywords
- efficient influence function
- uniform stochastic expansion
- nonparametric residuals
- estimated score function