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The discovery of mean square error consistency of a ridge estimator

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  • Luo, June

Abstract

A ridge estimator has been known for its superiority over the least squares estimator. In classical asymptotic theory dealing with the number of variables p fixed and the sample size n-->[infinity], the ridge estimator is a biased estimator. Recently, high dimensional data, such as microarray, exhibits a very high dimension p and a much smaller sample size n. There are discussions about the behavior of the ridge estimator when both p and n tend to [infinity], but very few dealing with n fixed and p-->[infinity]. The latter situation seems more relevant to microarray data in practice. Here we outline and describe the asymptotic properties of the ridge estimator when the sample size n is fixed and the dimension p-->[infinity]. Under certain regularity conditions, mean square error (MSE) consistency of the ridge estimator is established. We also propose a variable screening method to eliminate variables which are unrelated to the outcome and prove the consistency of the screening procedure.

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  • Luo, June, 2010. "The discovery of mean square error consistency of a ridge estimator," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 343-347, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:343-347
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    References listed on IDEAS

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    1. Shao, Jun & Chow, Shein-Chung, 2007. "Variable screening in predicting clinical outcome with high-dimensional microarrays," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1529-1538, September.
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    Cited by:

    1. Mohammad Arashi & Mina Norouzirad & Mahdi Roozbeh & Naushad Mamode Khan, 2021. "A High-Dimensional Counterpart for the Ridge Estimator in Multicollinear Situations," Mathematics, MDPI, vol. 9(23), pages 1-11, November.
    2. Luo, June, 2012. "Asymptotic efficiency of ridge estimator in linear and semiparametric linear models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 58-62.
    3. Luo, June & Kulasekera, K.B., 2013. "Error covariance matrix estimation using ridge estimator," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 257-264.

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    1. Luo, June & Kulasekera, K.B., 2013. "Error covariance matrix estimation using ridge estimator," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 257-264.
    2. Luo, June, 2012. "Asymptotic efficiency of ridge estimator in linear and semiparametric linear models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 58-62.

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