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

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  • Wang, Qihua

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.

Suggested Citation

  • Wang, Qihua, 2003. "Dimension reduction in partly linear error-in-response models with validation data," Journal of Multivariate Analysis, Elsevier, vol. 85(2), pages 234-252, May.
    • Handle: RePEc:eee:jmvana:v:85:y:2003:i:2:p:234-252
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    References listed on IDEAS

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    1. Sepanski, J. H. & Carroll, R. J., 1993. "Semiparametric quasilikelihood and variance function estimation in measurement error models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 223-256, July.
    2. Wang, Qihua, 1999. "Estimation of Partial Linear Error-in-Variables Models with Validation Data," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 30-64, April.
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    Cited by:

    1. Song, Weixing, 2009. "Lack-of-fit testing in errors-in-variables regression model with validation data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 765-773, March.
    2. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    3. Wang, Qihua, 2006. "Nonparametric regression function estimation with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1142-1161, May.

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