Estimation of Partial Linear Error-in-Variables Models with Validation Data

✍ Scribed by Qihua Wang

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 217 KB
• Volume: 69
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.1998.1797

✦ Synopsis

Consider the partial linear models of the form Y=X { ;+ g(T)+e, where the p-variate explanatory X is erroneously measured, and both T and the response Y are measured exactly. Let X be the surrogate variable for X with measurement error. Let the primary data set be that containing independent observations on (Y, X , T ) and the validation data set be that containing independent observations on (X, X , T ), where the exact observations on X may be obtained by some expensive or difficult procedures for only a small subset of subjects enrolled in the study. In this paper, without specifying any structure equation and the distribution assumption of X given X , a semiparametric method with the primary data is employed to obtain the estimators of ; and g( } ) based on the least-squares criterion with the help of validation data. The proposed estimators are proved to be strongly consistent. The asymptotic representation and the asymptotic normality of the estimator of ; are derived, respectively. The rate of the weak consistency of the estimator of g( } ) is also obtained.