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

✍ Scribed by Qihua Wang

• Book ID: 104269859
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 220 KB
• Volume: 85
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1016/s0047-259x(02)00066-0

✦ Synopsis

Consider partial linear models of the form Y ¼ X t b þ gðTÞ þ e with Y measured with error and both p-variate explanatory X and T measured exactly. Let Ỹ be the surrogate variable for Y with measurement error. Let primary data set be that containing independent observations on ð Ỹ; X ; TÞ and the validation data set be that containing independent observations on ðY ; Ỹ; X ; TÞ; 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 Ỹ; a semiparametric dimension reduction technique is employed to obtain estimators of b and gðÁÞ based the least squared method and kernel method with the primary data and validation data. The proposed estimators of b are proved to be asymptotically normal, and the estimator for gðÁÞ is proved to be weakly consistent with an optimal convergent rate.