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Showing 2 results for Hesamian
Dr. Mehdi Shams, Dr. Gholamreza Hesamian,
Volume 24, Issue 1 (9-2019)
Abstract
In this paper after introduce Ito integral we discuss filtering problem. In filtering problem there are two stochastic differential equations (system and observation) that given the observations we must find the best estimate for the random process of the system based on these observations. At last we give some useful examples.
Dr. Mehdi Shams, Dr. Gholamreza Hesamian,
Volume 27, Issue 1 (3-2023)
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.
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