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 datadependent 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.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)