1
Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran
2
Department of Statistics, Faculty of Mathematical Sciences, Payame Noor University, Tehran, Iran
Abstract
Information inequalities have many applications in estimation theory and statistical decision making. This paper describes the application of an information inequality to make the minimax decision in the framework of Bayesian theory. In this way, first a fundamental inequality for Bayesian risk is introduced under the square error loss function and then its applications are expressed in determining asymptotically and locally minimax estimators in the case of univariate and multivariate. In the case that the parameter components are orthogonal, the asymptotic-local minimax estimators are obtained for a function of the mean vector and the covariance matrix in the multivariate normal distribution. In the end, the bounds of information inequality are calculated under a general loss function.
Shams, M. & Hesamian, G. (2022). Asymptomatically-Locally minimax estimation for multivariate normal
distribution parameters. Andishe_ye Amari, 27(1), 113-126.
MLA
Shams, M., & Hesamian, G. "Asymptomatically-Locally minimax estimation for multivariate normal
distribution parameters", Andishe_ye Amari, 27, 1, 2022, 113-126.
HARVARD
Shams M., Hesamian G. (2022). 'Asymptomatically-Locally minimax estimation for multivariate normal
distribution parameters', Andishe_ye Amari, 27(1), pp. 113-126.
CHICAGO
M. Shams & G. Hesamian, "Asymptomatically-Locally minimax estimation for multivariate normal
distribution parameters," Andishe_ye Amari, 27 1 (2022): 113-126,
VANCOUVER
Shams M., Hesamian G. Asymptomatically-Locally minimax estimation for multivariate normal
distribution parameters. Andishe_ye Amari. 2022;27(1):113-126 (In Persian).
