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Inference on a regression model with noised variables and serially correlated errors

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  • You, Jinhong
  • Zhou, Xian
  • Zhu, Li-Xing

Abstract

Motivated by a practical problem, [Z.W. Cai, P.A. Naik, C.L. Tsai, De-noised least squares estimators: An application to estimating advertising effectiveness, Statist. Sinica 10 (2000) 1231-1243] proposed a new regression model with noised variables due to measurement errors. In this model, the means of some covariates are nonparametric functions of an auxiliary variable. They also proposed a de-noised estimator for the parameters of interest, and showed that it is root-n consistent and asymptotically normal when undersmoothing is applied. The undersmoothing, however, causes difficulty in selecting the bandwidth. In this paper, we propose an alternative corrected de-noised estimator, which is asymptotically normal without the need for undersmoothing. The asymptotic normality holds over a fairly wide range of bandwidth. A consistent estimator of the asymptotic covariance matrix under a general stationary error process is also proposed. In addition, we discuss the fitting of the error structure, which is important for modeling diagnostics and statistical inference, and extend the existing error structure fitting method to this new regression model. A simulation study is made to evaluate the proposed estimators, and an application to a set of advertising data is also illustrated.

Suggested Citation

  • You, Jinhong & Zhou, Xian & Zhu, Li-Xing, 2009. "Inference on a regression model with noised variables and serially correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1182-1197, July.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:6:p:1182-1197
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    3. Keener, Robert W. & Kmenta, Jan & Weber, Neville C., 1991. "Estimation of the Covariance Matrix of the Least-Squares Regression Coefficients When the Disturbance Covariance Matrix Is of Unknown Form," Econometric Theory, Cambridge University Press, vol. 7(1), pages 22-45, March.
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    Cited by:

    1. Cui, Hengjian & Hu, Tao, 2011. "On nonlinear regression estimator with denoised variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1137-1149, February.

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