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January, 1974 Rate of Convergence in the Sequence-Compound Squared-Distance Loss Estimation Problem for a Family of $m$-Variate Normal Distributions
V. Susarla
Ann. Statist. 2(1): 118-133 (January, 1974). DOI: 10.1214/aos/1176342618

Abstract

This paper is concerned with rates of convergence in the sequence-compound decision problem when the component problem is the squared-distance loss estimation of the mean of $m$-variate normal distribution with covariance matrix I. Section 1 introduces some notation and discusses the earlier work related to this problem. In Section 2, we prove two lemmas which are required in later sections. Sections 3, 4 and 5 exhibit sequence-compound decision procedures whose modified regrets are $O(n^{-1/m+4})$, near $O(n^{-\frac{1}{4}})$ and near $O(n^{-\frac{1}{2}})$ respectively, all the orders being uniform in parameter sequences concerned. In Section 6, comparisons have been made between the procedures given in Sections 3, 4 and 5. We conclude the paper with a few remarks.

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V. Susarla. "Rate of Convergence in the Sequence-Compound Squared-Distance Loss Estimation Problem for a Family of $m$-Variate Normal Distributions." Ann. Statist. 2 (1) 118 - 133, January, 1974. https://doi.org/10.1214/aos/1176342618

Information

Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0275.62007
MathSciNet: MR418301
Digital Object Identifier: 10.1214/aos/1176342618

Subjects:
Primary: 62C25
Secondary: 62C25 , 62C99

Keywords: decision theory , sequence-compound estimators , squared-distance loss estimation

Rights: Copyright © 1974 Institute of Mathematical Statistics

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