The existence of unbiased nonnegative definite quadratic estimates for linear combinations of variance covariance components is characterized by means of the natural parameter set in a residual model. In the presence of a quadratic subspace condition the following disjunction for nonnegative estimability is derived: either standard methods suffice, or the concepts of unbiasedness and nonnegative definiteness are incompatible. For the case of a single variance component it is shown that unbiasedness and nonnegative definiteness always entail a reduction to a trivial model in which the variance component under investigation is the sole remaining parameter. Several examples illustrate these results.
Publié le : 1981-03-14
Classification:
Negative estimates of variance,
unbiased nonnegative estimability,
quadratic subspaces of symmetric matrices,
MINQUE,
UMVU,
REML,
analysis of variance,
multivariate analysis,
62J10
@article{1176345395,
author = {Pukelsheim, Friedrich},
title = {On the Existence of Unbiased Nonnegative Estimates of Variance Convariance Components},
journal = {Ann. Statist.},
volume = {9},
number = {1},
year = {1981},
pages = { 293-299},
language = {en},
url = {http://dml.mathdoc.fr/item/1176345395}
}
Pukelsheim, Friedrich. On the Existence of Unbiased Nonnegative Estimates of Variance Convariance Components. Ann. Statist., Tome 9 (1981) no. 1, pp. 293-299. http://gdmltest.u-ga.fr/item/1176345395/