Estimation of a parameter vector when some components are restricted

✍ Scribed by Dominique Fourdrinier; Idir Ouassou; William E. Strawderman

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 196 KB
• Volume: 86
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1016/s0047-259x(02)00045-3

✦ Synopsis

We consider the problem of estimating a p-dimensional parameter y ¼ ðy 1 ; y; y p Þ when the observation is a p þ k vector ðX ; UÞ where dim X ¼ p and where U is a residual vector with dim U ¼ k: The distributional assumption is that ðX ; UÞ has a spherically symmetric distribution around ðy; 0Þ: Two restrictions on the parameter y are considered. First we assume that y i X0 for i ¼ 1; y; p and, secondly, we suppose that only a subset of these y i are nonnegative. For these two settings, we give a class of estimators dðX ; UÞ ¼ d 0 ðX Þ þ gðX ÞU 0 U which dominate, under the usual quadratic loss, a natural estimator d 0 ðX Þ which corresponds to the MLE in the normal case. Lastly, we deal with the situation where the parameter y belongs to a cone C of R p : We show that, under suitable condition, domination of the natural estimator adapted to this problem can be extended to a larger cone containing C and to any orthogonal transformation of this cone.