Local Asymptotic Normality of Statistical Experiments and Its Role in the Theory of Estimation and Testing of Hypotheses
Abstract
The main problem of the theory of estimation is to find optimal estimates for the unknown parameters. There are two approaches to solving those problems: an approach based on a sample of the finite size and the asymptotic approach, based on a sample of the growing size. The asymptotic approaches can exhibit the properties of optimality as n → ∞. One of them is the approach of asymptotic minimax estimates. This property is called the local asymptotic minimax estimates and is based on the asymptotic behavior of the sequence of statistical experiments at approaching sequences of alternative hypotheses. In this paper we consider the asymptotic normality of the estimates of Bayesian type and asymptotical minimax efficiency of maximum likelihood estimates using the property of the local asymptotic normality of the likelihood ratio statistics in a model ofrandom censoring from both sides.
About the Authors
A. A. Abdushukurov
Национальный университет Узбекистана им. М. Улугбека
Russian Federation
Russian Federation
N. S. Nurmukhamedova
Национальный университет Узбекистана им. М. Улугбека
Russian Federation
Russian Federation
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Review
For citations:
Abdushukurov A.A., Nurmukhamedova N.S. Local Asymptotic Normality of Statistical Experiments and Its Role in the Theory of Estimation and Testing of Hypotheses. Industrial laboratory. Diagnostics of materials. 2016;82(3):74-79. (In Russ.)
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