Dimension reduction in partly linear error-in-response models with validation data

Qihua Wang

Journal of Multivariate Analysis, 2003, vol. 85, issue 2, 234-252

Abstract: Consider partial linear models of the form Y=X[tau][beta]+g(T)+e with Y measured with error and both p-variate explanatory X and T measured exactly. Let be the surrogate variable for Y with measurement error. Let primary data set be that containing independent observations on and the validation data set be that containing independent observations on , where the exact observations on Y 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 equations and distribution assumption of Y given , a semiparametric dimension reduction technique is employed to obtain estimators of [beta] and g(·) based the least squared method and kernel method with the primary data and validation data. The proposed estimators of [beta] are proved to be asymptotically normal, and the estimator for g(·) is proved to be weakly consistent with an optimal convergent rate.

Keywords: Dimension; reduction; Partial; linear; model; Validation; data; Asymptotic; normality (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (3)

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