New estimation for heteroscedastic single-index measurement error models. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Ding, Hui; Zhang, Riquan; Zhu, Hanbing
• Is Part Of: Journal of nonparametric statistics. Volume 34:Issue 1(2022)
• Page Start: 95
• Page End: 112
• Publication Date: 2022-01-02
• Subjects: Corrected quantile loss function -- heteroscedasticity -- linearity condition -- measurement error -- single-index model; 62G05; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2021.2025238
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : In this paper, we propose a novel estimation for heteroscedastic single-index models with covariate measurement errors, in which both the conditional mean and conditional variance functions of the response given the covariates have a single-index structure. When covariates are directly observable, we show that the index parameter vector can be estimated consistently by the estimation obtained by fitting a misspecified linear quantile regression model under some mild regularity conditions. It is well known that naively treating mismeasured covariates as error-free usually leads to inconsistent estimators. To account for measurement errors in covariates, we establish a new estimation procedure based on corrected quantile loss function, and obtain the asymptotic consistency and normality of the resulting estimators. Finally, the finite sample performance of the proposed estimation method is illustrated by simulation studies and an empirical analysis of a real dataset.