Orthogonal Series Estimation of Nonparametric Regression Measurement Error Models with Validation Data

Zanhua Yin

doi:10.4236/am.2017.812130

Abstract

In this article we study the estimation method of nonparametric regression measurement error model based on a validation data. The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption. The convergence rates of the proposed estimator are derived. By example and through simulation, the method is robust against the misspecification of a measurement error model.

Highlights

Let Y be a scalar response variable and X be an explanatory variable in regression
In this article we study the estimation method of nonparametric regression measurement error model based on a validation data
The estimation procedures are based on orthogonal series estimation and truncated series approximation methods without specifying any structure equation and the distribution assumption

Summary

Introduction

Let Y be a scalar response variable and X be an explanatory variable in regression. We consider the nonparametric regression model. The relationship between the surrogate variables and the true variables can be rather complicated compared to the classical or Berkson error structural equations usually assumed. This situation presents serious difficulties in making valid statistical inferences. [3]-[12] and among others) These approaches do not applicable for handling nonparametric regression measurement error model with the availability of a validation data set. Developed estimation methods for the nonparametric regression model (1) with measurement error. Without specifying any structural equations, an orthogonal series method is proposed to estimate g with the help of validation data.

Orthogonal Series Estimation

Theoretical Properties

Simulation Studies

Discussion