Estimation of partial linear error-in-variables models with validation data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:69

Article

Wang, QH

关键词: partial linear model;    validation data;    strong consistency;    asymptotic representation;    asymptotic normality;   

DOI  :  10.1006/jmva.1998.1797

来源: Elsevier

【 摘 要 】

Consider the partial linear models of the form Y = X(t)beta + g(T) + e, where the p-variate explanatory Xis erroneously measured, and both T and the response Y are measured exactly. Let (X) over tilde be the surrogate variable for X with measurement error. Let the primary data set be that containing independent observations on (Y, (X) over tilde T) and the validation data set be that containing independent observations on (X, (X) over tilde, 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) over tilde, a semiparametric method with the primary data is employed to obtain the estimators of beta 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 beta are derived, respectively. The rate of the weak consistency of the estimator of g(.) is also obtained, (C) 1999 Academic Press.

【 授权许可】

Free