TY - JOUR
T1 - Improved estimates of location in the presence of an unknown scale
AU - Brandwein, Ann Cohen
AU - Strawderman, William E.
N1 - Funding Information:
Received August 15, 1990; revised March 8, 1991. AMS subject classifications: 62C99, 62F10, 62899. Key words and phrases: spherical symmetry, quadratic loss, concave loss, James-Stein estimation, location parameter, unknown scale, superharmonic functions. * Research supported by NSF DMS-88-22622. 305
PY - 1991/11
Y1 - 1991/11
N2 - We investigate conditions under which estimators of the form X + aU′Ug(X) dominate X when X, a p × 1 vector, and U, an m × 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]′ σ has a spherically symmetric distribution about [θ1, θ2,..., θp, 0, 0,..., 0]′, where σ is an unknown scale. Brandwein and Strawderman [2] have results for quadratic loss and we extend these results to concave functions of quadratic loss and to general quadratic loss.
AB - We investigate conditions under which estimators of the form X + aU′Ug(X) dominate X when X, a p × 1 vector, and U, an m × 1 vector, are distributed such that [X1, X2,..., Xp, U1, U2,..., Up]′ σ has a spherically symmetric distribution about [θ1, θ2,..., θp, 0, 0,..., 0]′, where σ is an unknown scale. Brandwein and Strawderman [2] have results for quadratic loss and we extend these results to concave functions of quadratic loss and to general quadratic loss.
KW - James-Stein estimation
KW - concave loss
KW - location parameter
KW - quadratic loss
KW - spherical symmetry
KW - superharmonic functions
KW - unknown scale
UR - https://www.scopus.com/pages/publications/0000058766
UR - https://www.scopus.com/pages/publications/0000058766#tab=citedBy
U2 - 10.1016/0047-259X(91)90103-9
DO - 10.1016/0047-259X(91)90103-9
M3 - Article
AN - SCOPUS:0000058766
SN - 0047-259X
VL - 39
SP - 305
EP - 314
JO - Journal of Multivariate Analysis
JF - Journal of Multivariate Analysis
IS - 2
ER -