Publication Type
Journal Article
Version
publishedVersion
Publication Date
12-2015
Abstract
In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton-Raphson estimator and the local profile likelihood estimator are investigated. We show that the proposed estimators are asymptotically equivalent to the infeasible local likelihood estimators [e.g., Aerts and Claeskens (1997) Journal of the American Statistical Association 92, 1536-1545], which require knowledge of the error distribution. Simulation evidence suggests that when the distribution of the error term is different from Gaussian, the adaptive estimators of both conditional mean and variance can often achieve significant efficiency over the conventional local polynomial estimators.
Keywords
Adaptive Estimation, Conditional Heteroskedasticity, Local Profile Likelihood Estimation, Local Polynomial Estimation, Nonparametric Regression, One-step Estimator
Discipline
Econometrics
Research Areas
Econometrics
Publication
Econometric Theory
Volume
31
Issue
6
First Page
1153
Last Page
1191
ISSN
0266-4666
Identifier
10.1017/S0266466614000450
Publisher
Cambridge University Press
Citation
JIN, Sainan; SU, Liangjun; and XIAO, Zhijie.
Adaptive nonparametric regression with conditional heteroskedasticity. (2015). Econometric Theory. 31, (6), 1153-1191.
Available at: https://ink.library.smu.edu.sg/soe_research/1878
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1017/S0266466614000450