On estimation in multivariate linear calibration with elliptical errors |
| |
Authors: | Hisayuki Tsukuma |
| |
Institution: | (1) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106-8569 Tokyo, Japan |
| |
Abstract: | The estimation problem in multivariate linear calibration with elliptical errors is considered under a loss function which
can be derived from the Kullback-Leibler distance. First, we discuss the problem under normal errors and give unbiased estimate
of risk of an alternative estimator by means of the Stein and Stein-Haff identities for multivariate normal distribution.
From the unbiased estimate of risk, it is shown that a shrinkage estimator improves on the classical estimator under the loss
function. Furthermore, from the extended Stein and Stein-Haff identities for our elliptically contoured distribution, the
above result under normal errors is extended to the estimation problem under elliptical errors. We show that the shrinkage
estimator obtained under normal models is better than the classical estimator under elliptical errors with the above loss
function and hence we establish the robustness of the above shrinkage estimator. |
| |
Keywords: | Elliptically contoured distribution Kullback-Leibler distance multivariate linear model shrinkage estimator |
本文献已被 SpringerLink 等数据库收录! |
|