JAMES-STEIN TYPE ESTIMATORS IN LARGESAMPLES WITH APPLICATION TO THE LEASTABSOLUTE DEVIATION ESTIMATOR

We explore the extension of James-Stein type estimators in a direction that enables them topreserve their superiority when the sample size goes to infinity. Instead of shrinking a base estimatortowards a fixed point, we shrink it towards a data-dependent point. We provide an analytic expression forthe asymptotic risk and bias of James-Stein type estimators shrunk towards a data-dependent point andprove that they have smaller asymptotic risk than the base estimator. Shrinking an estimator toward adata-dependent point turns out to be equivalent to combining two random variables using the James-Steinrule. We propose a general combination scheme which includes random combination (the James-Steincombination) and the usual nonrandom combination as special cases. As an example, we apply ourmethod to combine the Least Absolute Deviations estimator and the Least Squares estimator...<br<