Estimation of Nonparametric Regression Models with Measurement Error Using Validation Data

• 作者: Fang Liu Zanhua Yin
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: ILL-POSED INVERSE PROBLEMS Measurement ERRORS NONPARAMETRIC Regression ORTHOGONAL Series
• 年，卷（期）: 2017,（10）
• 页码范围: 1454-1463
• 页数: 10页
• 分类号: O1

摘要

We consider the problem of estimating a function g in nonparametric regression model when only some of covariates are measured with errors with the assistance of validation data. Without specifying any error model structure between the surrogate and true covariables, we propose an estimator which integrates orthogonal series estimation and truncated series approximation method. Under general regularity conditions, we get the convergence rate of this estimator. Simulations demonstrate the finite-sample properties of the new estimator.