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Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model

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  • Arashi, M.
  • Kibria, B.M. Golam
  • Norouzirad, M.
  • Nadarajah, S.

Abstract

Recently, Liu (1993) estimator draws an important attention to estimate the regression parameters for an ill-conditioned linear regression model when the vector of errors is distributed according to the law belonging to the class of elliptically contoured distributions (ECDs). This paper proposed some improved Liu type estimators, namely, the unrestricted Liu estimator (ULE), restricted Liu estimator (RLE), preliminary test Liu estimator (PTLE), shrinkage Liu estimator (SLE) and positive rule Liu estimator (PRLE) for estimating the regression parameters β. The performance of the proposed estimators is compared based on the quadratic bias and risk functions under both null and alternative hypotheses, which specify certain restrictions on the regression parameters. The conditions of superiority of the proposed estimators for parameter d and non-centrality parameter Δ are given.

Suggested Citation

  • Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
    • Handle: RePEc:eee:jmvana:v:126:y:2014:i:c:p:53-74
    DOI: 10.1016/j.jmva.2014.01.002
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    References listed on IDEAS

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    Cited by:

    1. M. Arashi & Mahdi Roozbeh, 2019. "Some improved estimation strategies in high-dimensional semiparametric regression models with application to riboflavin production data," Statistical Papers, Springer, vol. 60(3), pages 667-686, June.
    2. Roozbeh, Mahdi, 2018. "Optimal QR-based estimation in partially linear regression models with correlated errors using GCV criterion," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 45-61.
    3. Roozbeh, Mahdi, 2015. "Shrinkage ridge estimators in semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 56-74.
    4. Roozbeh, Mahdi, 2016. "Robust ridge estimator in restricted semiparametric regression models," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 127-144.
    5. Mohammad Arashi & Mina Norouzirad & S. Ejaz Ahmed & Bahadır Yüzbaşı, 2018. "Rank-based Liu regression," Computational Statistics, Springer, vol. 33(3), pages 1525-1561, September.
    6. Sivarajah Arumairajan & Pushpakanthie Wijekoon, 2017. "The generalized preliminary test estimator when different sets of stochastic restrictions are available," Statistical Papers, Springer, vol. 58(3), pages 729-747, September.

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