Improved estimation for elliptically symmetric distributions with unknown block diagonal covariance matrix
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 = 1 U´j∑-1 Uj) 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 - 1Uij U´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.
Year of publication: |
2009
|
---|---|
Authors: | Dominique, Fourdrinier ; Strawderman William E. ; Wells Martin T. |
Published in: |
Statistics & Risk Modeling. - De Gruyter. - Vol. 26.2009, 3, p. 203-217
|
Publisher: |
De Gruyter |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
ESTIMATION OF THE MEAN OF A e1-EXPONENTIAL MULTIVARIATE DISTRIBUTION
Dominique, Fourdrinier, (2000)
-
Dan, Kucerovsky, (2009)
-
ε- SOLUTIONS OF MINIMIZATION PROBLEMS IN STATISTICS
Wells Martin T., (1991)
- More ...