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ADAPTIVE NONPARAMETRIC REGRESSION WITH CONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  08 September 2014

Sainan Jin ,
Liangjun Su  and
Zhijie Xiao
Sainan Jin*
Affiliation:
Singapore Management University
Liangjun Su
Affiliation:
Singapore Management University
Zhijie Xiao
Affiliation:
Boston College
*
*Address correspondence to Sainan Jin, School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903; e-mail: snjin@smu.edu.sg.
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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.

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ARTICLES
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Econometric Theory , Volume 31 , Issue 6 , December 2015 , pp. 1153 - 1191
Copyright
Copyright © Cambridge University Press 2014 

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