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Limit expressions for the risk of james‐stein estimators
Author(s) -
Casella George,
Hwang Jiunn Tzon
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3556196
Subject(s) - limit (mathematics) , estimator , mathematics , simple (philosophy) , dimension (graph theory) , james–stein estimator , statistics , calculus (dental) , minimax estimator , combinatorics , mathematical analysis , philosophy , minimum variance unbiased estimator , epistemology , medicine , dentistry
Limit expressions (as the dimension p ← ∞ ) are derived for the relative risk of the James‐Stein estimator and its positive‐part version. The limit is simple to evaluate, and gives the amount of improvement in risk that is possible. The technique used is to bound the risk, both above and below. with bounds that converge to the same limit. For the James‐Stein estimator these bounds are simple to calculate, and are quite accurate even for moderate dimensions.