Statistical inference for a single-index varying coefficient model with measurement errors in all covariates

Abstract

In this paper, a single-index varying coefficient model with measurement errors in all covariates is investigated. We propose a new approach to estimate the link function $g(\cdot )$ and the index parameter β, which combines the simulation-extrapolation (SIMEX) technique with local linear regression and estimating equation. Under some regularity conditions, large sample properties of the proposed estimators are established. Simulation studies and an application are presented to evaluate the proposed method.

Keywords:

• Bias-corrected estimate
• local linear regression
• measurement errors
• SIMEX technique
• single-index varying coefficient model

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant numbers 11471160, 11101114] and the Humanities and Social Science Fund of Ministry of Education of China [grant number 21YJA910004].