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Rank-based ridge estimation in multiple linear regression

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  • Asuman Turkmen
  • Omer Ozturk

Abstract

Multicollinearity and model misspecification are frequently encountered problems in practice that produce undesirable effects on classical ordinary least squares (OLS) regression estimator. The ridge regression estimator is an important tool to reduce the effects of multicollinearity, but it is still sensitive to a model misspecification of error distribution. Although rank-based statistical inference has desirable robustness properties compared to the OLS procedures, it can be unstable in the presence of multicollinearity. This paper introduces a rank regression estimator for regression parameters and develops tests for general linear hypotheses in a multiple linear regression model. The proposed estimator and the tests have desirable robustness features against the multicollinearity and model misspecification of error distribution. Asymptotic behaviours of the proposed estimator and the test statistics are investigated. Real and simulated data sets are used to demonstrate the feasibility and the performance of the estimator and the tests.

Suggested Citation

  • Asuman Turkmen & Omer Ozturk, 2014. "Rank-based ridge estimation in multiple linear regression," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 737-754, December.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:4:p:737-754
    DOI: 10.1080/10485252.2014.964714
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    References listed on IDEAS

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    1. Paul W. Holland, 1973. "Weighted Ridge Regression: Combining Ridge and Robust Regression Methods," NBER Working Papers 0011, National Bureau of Economic Research, Inc.
    2. Horowitz, Joel L & Spokoiny, Vladimir G, 2001. "An Adaptive, Rate-Optimal Test of a Parametric Mean-Regression Model against a Nonparametric Alternative," Econometrica, Econometric Society, vol. 69(3), pages 599-631, May.
    3. Brent Johnson & Limin Peng, 2008. "Rank-based variable selection," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(3), pages 241-252.
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    Cited by:

    1. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.

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