James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator

Tae-Hwan Kim () and Halbert White

University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego

Abstract: We explore the extension of James-Stein type estimators in a direction that enables them to preserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimator towards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression for the asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point and prove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward a data-dependent point turns out to be equivalent to combining two random variables using the James-Stein rule. We propose a general combination scheme which includes random combination (the James-Stein combination) and the usual nonrandom combination as special cases. As an example, we apply our method to combine the Least Absolute Deviations estimator and the Least Squares estimator. Our simulation study indicates that the resulting combination estimators have desirable finite sample properties when errors are drawn from symmetric distributions. Finally, using stock return data we present some empirical evidence that the combination estimators have the potential to improve out-of-sample prediction in terms of both mean square error and mean absolute error.

Keywords: shrinkage; asymptotic risk; combination estimator (search for similar items in EconPapers)
Date: 2000-05-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.escholarship.org/uc/item/4zq9k3qh.pdf;origin=repeccitec (application/pdf)

Related works:
Journal Article: James-Stein-Type Estimators in Large Samples With Application to the Least Absolute Deviations Estimator (2001)
Working Paper: James-Stein Type Estimator in Large Samples with Application to the Least Absolute Deviations Estimator (2000)
Working Paper: James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator (1999)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:cdl:ucsdec:qt4zq9k3qh

Access Statistics for this paper

More papers in University of California at San Diego, Economics Working Paper Series from Department of Economics, UC San Diego Contact information at EDIRC.
Bibliographic data for series maintained by Lisa Schiff ().