In this article, we investigate how to apply the empirical likelihood method for the inference of average derivatives in nonparametric multiple regression models. Empirical likelihood ratios for the vectors of the average derivatives and the density-weighted average derivatives are defined and it is shown that their limiting distributions are weighted sums of independent chi-squared random variables with one degree of freedom. Monte Carlo simulation studies are presented to compare the empirical likelihood method with the normal-approximation-based method. It is found that the empirical likelihood method performs better than the normal-approximation-based method.
Bibliographical noteFunding Information:
The authors wish to thank the associate editor for bringing their attention to the density-weighted average derivative estimation by Powell et al. , the editor, the associate editor and one referee for their insightful and constructive comments that have helped greatly in improving the article, and Professor Murray Burke for his careful reading of the article and his comments. Lu’s research was partly supported by the NSERC Discovery Grant 73-1069 of Canada and Qi’s research was supported by NSF Grant DMS-0604176.
- Average derivative
- Empirical likelihood
- Kernel estimation
- Nonparametric regression
- Single-index model