Complete consistency for the weighted least squares estimators in semiparametric regression models

Yutan Lv, Yunbao Yao, Jun Zhou, Xiaoqin Li, Ruiqi Yang and Xuejun Wang

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 22, 7797-7818

Abstract: In this article, we consider the semiparametric regression model yi=xiβ+g(ti)+σiei, i=1,2,…,n, where σi2=f(ui), (xi,ti,ui) are known fixed design points, β is an unknown parameter to be estimated, g(·) and f(·) are unknown functions defined on a compact set. Assume that the random errors {ei, i≥1} are zero mean widely orthant dependent (WOD, for short) random variables. Under some suitable conditions, we investigate the complete consistency for the least squares estimators (LSE, for short) and the weighted least squares estimators (WLSE, for short) of β and g(·). In addition, a numerical simulation is given to study the numerical performance based on finite samples.

Date: 2023
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DOI: 10.1080/03610926.2022.2050400

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