 The discovery of mean square error consistency of a ridge estimatorJune Luo Statistics & Probability Letters, 2010, vol. 80, issue 5-6, 343-347 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. Date: 2010 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:80:y:2010:i:5-6:p:343-347 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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