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A ridge regression estimation approach to the measurement error model

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  • Saleh, A.K.Md. Ehsanes
  • Shalabh,

Abstract

This paper considers the estimation of the parameters of measurement error models where the estimated covariance matrix of the regression parameters is ill conditioned. We consider the Hoerl and Kennard type (1970) ridge regression (RR) modifications of the five quasi-empirical Bayes estimators of the regression parameters of a measurement error model when it is suspected that the parameters may belong to a linear subspace. The modifications are based on the estimated covariance matrix of the estimators of regression parameters. The estimators are compared and the dominance conditions as well as the regions of optimality of the proposed estimators are determined based on quadratic risks.

Suggested Citation

  • Saleh, A.K.Md. Ehsanes & Shalabh,, 2014. "A ridge regression estimation approach to the measurement error model," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 68-84.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:68-84
    DOI: 10.1016/j.jmva.2013.08.014
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    References listed on IDEAS

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    1. Shalabh & Garg, Gaurav & Misra, Neeraj, 2009. "Use of prior information in the consistent estimation of regression coefficients in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1498-1520, August.
    2. Jurecková, Jana & Picek, Jan & Saleh, A.K.Md. Ehsanes, 2010. "Rank tests and regression rank score tests in measurement error models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3108-3120, December.
    3. Shalabh, 1998. "Improved Estimation in Measurement Error Models Through Stein Rule Procedure," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 35-48, October.
    4. Kim, H.M. & Saleh, A.K.Md.Ehsanes, 2005. "Improved estimation of regression parameters in measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 273-300, August.
    5. B. M. Golam Kibria & A. K. Md. E. Saleh, 2004. "Preliminary test ridge regression estimators with student’s t errors and conflicting test-statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 105-124, May.
    6. A. Saleh & B. Golam Kibria, 2011. "On some ridge regression estimators: a nonparametric approach," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 819-851.
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    Cited by:

    1. Huang, Chao & Farewell, Daniel & Pan, Jianxin, 2017. "A calibration method for non-positive definite covariance matrix in multivariate data analysis," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 45-52.

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