Statistical inference for heteroscedastic semi-varying coefficient EV models

ABSTRACT

This paper proposes an estimation procedure for a class of semi-varying coefficient regression models when the covariates of the linear part are subject to measurement errors. Initial estimates for the regression and varying coefficients are first constructed by the profile least-squares procedure without input from heteroscedasticity, a bias-corrected kernel estimate for the variance function then is proposed, which in turn is used to define re-weighted bias-corrected estimates of the regression and varying coefficients. Large sample properties of the proposed estimates are thoroughly investigated. The finite-sample performance of the proposed estimates is assessed by an extensive simulation study and an application to the Boston housing data set. The simulation results show that the re-weighted bias-corrected estimates outperform the initial estimates and the naive estimates.

KEYWORDS:

• Asymptotic normality
• consistency
• heteroscedasticity
• profile least squares
• semi-varying coefficient EV model.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F35
• Secondary 62F10

Acknowledgments

Jianhong Shi’s research is supported by the Natural Science Foundation of Shanxi Province, China [grant number 2013011002-1], and Weixing Song’s research is partly supported by the NSF DMS [grant number 1205276]. The authors would like to thank the editor, the associate editor, and the referees for their valuable suggestions that greatly improved the manuscript.

Additional information

Funding

Armenian National Science and Education Fund [NSF DMS 1205276]; Natural Science Foundation of Shanxi Province [2013011002-1].