Statistical estimation for single-index varying-coefficient models with multiplicative distortion measurement errors. Issue 4 (4th July 2021)

• Record Type: Journal Article
• Authors: Huang, Zhensheng; Lou, Wen; Meng, Shuyu
• Is Part Of: Statistics. Volume 55:Issue 4(2021)
• Page Start: 851
• Page End: 874
• Publication Date: 2021-07-04
• Subjects: Single-index varying-coefficient model -- multiplicative distortion measurement errors -- conditional absolute mean calibration -- estimating equation -- local linear smoothing; 62G10 -- 62H20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1980794
• Languages: English
• ISSNs: 0233-1888

Abstract

Abstract : During the observation, various factors can cause variables to be contaminated by measurement errors. In this paper, we consider the estimation for single-index varying-coefficient models where both the response variable and covariates are measured with multiplicative distortion measurement errors. First, we use the conditional absolute mean calibration to calibrate the distorted variables. Based on the calibrated variables, we obtain the estimators of the parameters and coefficient functions by local linear smoothing and estimating equations. Furthermore, we prove that the obtained estimators have asymptotic normality and the estimator of parametric component is still root- n consistent. Finally, two simulation examples and the analysis of body fat data are given to illustrate that the proposed estimators are unbiased, robust and practical.