Estimation of scatter matrix based on i.i.d. sample from elliptical distributions

Kaitai Fang, Runze Li

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

In this paper, we consider the estimation of a scatter matrix under entropy loss, quadratic loss, when the samples x(1),... x(n) are i.i.d. and x(1)∼ECp(μ,Σ,f). With respect to entropy and quadratic losses, we obtain the best estimator of Σ having the form αSx as well as having the form TxΔTx′, where Sx,Tx and Δ are given in the text, and obtain the minimax estimator of Σ and the best equivariant estimator of Σ with respect to the triangular transformations group LT+(p) (the group consisting of lower triangular matrices with positive diagonal elements). Some related discussion are given as its generalizations.

Original languageEnglish (US)
Pages (from-to)405-412
Number of pages8
JournalActa Mathematicae Applicatae Sinica
Volume11
Issue number4
DOIs
StatePublished - Oct 1 1995

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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