Effects of measurement error on a class of single-index varying coefficient regression models

This paper investigates the estimation in a class of single-index varying coefficient regression model when some covariates are contaminated with measurement errors. A bias-corrected least square procedure based on the observed data is proposed. By replacing the nonparametric single index part with a local linear approximation, an iterative algorithm for estimating the index parameter is proposed. More importantly, a special case is identified in which the naive procedure provides consistent estimates for the single index parameters. Large sample properties of the proposed estimators are established. The finite sample performance of the proposed estimators are evaluated by simulation studies.