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Applications of resampling methods in multivariate Liu estimator

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  • Shima Pirmohammadi

    (University of Isfahan)

  • Hamid Bidram

    (University of Isfahan)

Abstract

Multicollinearity among independent variables is one of the most common problems in regression models. The aftereffects of this problem, such as ill-conditioning, instability of estimators, and inflating mean squared error of ordinary least squares estimator (OLS), in the multivariate linear regression model (MLRM) are the same that of linear regression models. To combat multicollinearity, several approaches have been presented in the literature. Liu estimator (LE), as a well known estimator in this connection, has been used in linear, generalized linear, and nonlinear regression models by researchers in recent years. In this paper, for the first time, LE and jackknifed Liu estimator (JLE) are investigated in MLRM. To improve estimators in the sense of mean squared error, two known resampling methods, i.e., jackknife and bootstrap, are used. Finally, OLS, LE, and JLE are compared by a simulation study and also using a real data set, by resampling methods in MLRM.

Suggested Citation

  • Shima Pirmohammadi & Hamid Bidram, 2024. "Applications of resampling methods in multivariate Liu estimator," Computational Statistics, Springer, vol. 39(2), pages 677-708, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01316-2
    DOI: 10.1007/s00180-022-01316-2
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    References listed on IDEAS

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    1. Mori, Yuichi & Suzuki, Taiji, 2018. "Generalized ridge estimator and model selection criteria in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 243-261.
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    4. Nyquist, Hans, 1988. "Applications of the jackknife procedure in ridge regression," Computational Statistics & Data Analysis, Elsevier, vol. 6(2), pages 177-183, March.
    5. Eck, Daniel J., 2018. "Bootstrapping for multivariate linear regression models," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 141-149.
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