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Estimation in linear regression models with measurement errors subject to single-indexed distortion

Listed author(s):
  • Zhang, Jun
  • Gai, Yujie
  • Wu, Ping
Registered author(s):

    In this paper, we consider statistical inference for linear regression models when neither the response nor the predictors can be directly observed, but are measured with errors in a multiplicative fashion and distorted as single index models of observable confounding variables. We propose a semiparametric profile least squares estimation procedure to estimate the single index. Then we develop a global weighted least squares estimation procedure for parameters of linear regression models via the varying coefficient models. Asymptotic properties of the proposed estimators are established. The results combined with consistent estimators for the asymptotic variance can be employed to test whether the targeted parameters in the single index and linear regression models are significant. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are also applied to a dataset from a Pima Indian diabetes data study.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 59 (2013)
    Issue (Month): C ()
    Pages: 103-120

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    Handle: RePEc:eee:csdana:v:59:y:2013:i:c:p:103-120
    DOI: 10.1016/j.csda.2012.10.001
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    1. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single-index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570.
    2. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    3. Yingcun Xia & Howell Tong & W. K. Li & Li-Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410.
    4. Zhang, Jun & Zhu, Li-Ping & Zhu, Li-Xing, 2012. "On a dimension reduction regression with covariate adjustment," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 39-55, February.
    5. Wang, Tao & Xu, Pei-Rong & Zhu, Li-Xing, 2012. "Non-convex penalized estimation in high-dimensional models with single-index structure," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 221-235.
    6. Zhu, Lixing & Lin, Lu & Cui, Xia & Li, Gaorong, 2010. "Bias-corrected empirical likelihood in a multi-link semiparametric model," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 850-868, April.
    7. J. Fan & J.-T. Zhang, 2000. "Two-step estimation of functional linear models with applications to longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 303-322.
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