Improved estimation for elliptically symmetric distributions with unknown block diagonal covariance matrix

Fourdrinier Dominique, Strawderman William E. and Wells Martin T.

Statistics & Risk Modeling, 2009, vol. 26, issue 3, 203-217

Abstract: Let X, U1, …, Un-1 be n random vectors in ℝp with joint density of the form f((X - θ)´∑-1(X - θ) + ∑n-1j = 1U´j∑-1Uj) where both θ∈ℝp and ∑ are unknown, the scale matrix ∑ being supposed structured as a diagonal matrix, that is, ∑= diag(∑1, …,∑b) where, for 1 ≤ i ≤ b, ∑i is a pi × pi matrix and ∑i = 1bpi = p. We consider the problem of the estimation of θ with the invariant loss (δ - θ)´∑-1(δ - θ) and propose estimators which dominate the usual estimator δ0(X) = X. These domination results hold simultaneously for the entire class of such distributions. The proof uses a generalization of integration by parts formulae by Stein and Haff. We also consider estimating ∑ under LS(∑^,∑) = tr(∑^∑-1) - log |∑^∑-1| - p and propose estimators that dominate the unbiased estimator ∑^UB = diag(S1, …, Sb)/(n - 1), where Si = ∑j = 1n - 1UijU´ij and dim Uji = pi, for 1 ≤ i ≤ b and 1 ≤ j ≤ n - 1. The subsequent development of expressions is analogous to the unbiased estimators of risk technique and, in fact, reduces to an unbiased estimator of risk in the normal case.

Keywords: block diagonal; elliptically symmetric distributions; James-Stein estimation; location parameter; minimax (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1524/stnd.2008.1002 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:26:y:2009:i:3:p:203-217:n:4

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1524/stnd.2008.1002

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().