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Stein-type improvement under stochastic constraints: Use of multivariate Student-t model in regression

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  • Arashi, M.
  • Tabatabaey, S.M.M.

Abstract

Recently, many researchers have considered the use of heavy-tailed models for processing multiplicative economic and business data for validity of robustness. As a reliable justification, fat-tailed models contain outliers and extreme values reasonably well. In this paper, we assume in the multiple regression model, that the error vector follows multivariate Student-t distribution as a viable alternative to the multivariate normal and obtain unrestricted and restricted estimators under the suspicion of stochastic constraints occurring. Also the preliminary test, Stein-type shrinkage and positive-rule shrinkage estimators are derived when the variable term in the restriction is assumed to follow multivariate Student-t distribution. The conditions of superiority of the proposed estimators are provided under weighted quadratic loss function.

Suggested Citation

  • Arashi, M. & Tabatabaey, S.M.M., 2008. "Stein-type improvement under stochastic constraints: Use of multivariate Student-t model in regression," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2142-2153, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2142-2153
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    Cited by:

    1. A. Saleh & B. Kibria, 2013. "Improved ridge regression estimators for the logistic regression model," Computational Statistics, Springer, vol. 28(6), pages 2519-2558, December.
    2. Ren, Xingwei, 2014. "On the equivalence of the BLUEs under a general linear model and its restricted and stochastically restricted models," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 1-10.
    3. Arashi, M. & Tabatabaey, S.M.M., 2009. "Improved variance estimation under sub-space restriction," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1752-1760, September.

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