Shrinkage Domination in a Multivariate Common Mean Problem
George, Edward I.
Ann. Statist., Tome 19 (1991) no. 1, p. 952-960 / Harvested from Project Euclid
Consider the problem of estimating the $p \times 1$ mean vector $\theta$ under expected squared error loss, based on the observation of two independent multivariate normal vectors $Y_1 \sim N_p(\theta, \sigma^2I)$ and $Y_2 \sim N_p(\theta, \lambda\sigma^2I)$ when $\lambda$ and $\sigma^2$ are unknown. For $p \geq 3$, estimators of the form $\delta_\eta = \eta Y_1 + (1 - \eta)Y_2$ where $\eta$ is a fixed number in (0, 1), are shown to be uniformly dominated in risk by Stein estimators in spite of the fact that independent estimates of scale are unavailable. A consequence of this result is that when $\lambda$ is assumed known, shrinkage domination is robust to incorrect specification of $\lambda$.
Publié le : 1991-06-14
Classification:  Risk,  robustness,  shrinkage estimation,  Stein estimators,  62H12,  62C99,  62J07
@article{1176348130,
     author = {George, Edward I.},
     title = {Shrinkage Domination in a Multivariate Common Mean Problem},
     journal = {Ann. Statist.},
     volume = {19},
     number = {1},
     year = {1991},
     pages = { 952-960},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176348130}
}
George, Edward I. Shrinkage Domination in a Multivariate Common Mean Problem. Ann. Statist., Tome 19 (1991) no. 1, pp.  952-960. http://gdmltest.u-ga.fr/item/1176348130/