On lower bounds of the moderate and cramer type large deviation probabilities in statistical inference
- Ermakov, Mikhail S.
2010 Mathematics Subject Classification
- 62F05 62F12 62G20
- Moderate large deviations, Cramer type large deviations, asymptotic efficiency, asymptotically minimax estimation, asymptotically minimax hypothesis testing, Bahadur efficiency, Chernoff efficiency
We indicate new simple assignments of the lower bounds for the probabilities of the moderate and Cramer type large deviations of type I and type II errors of statistical tests. These assignments are based on a one natural property of the normal distribution. Using these results we deduce easily the lower bounds for the probabilities of the moderate and Cramer type large deviations of estimators. The lower bounds were obtained under the more weak assumptions then in the previous papers. The lower bound for the probabilities of the Cramer type large deviations of estimators has not been proved earlier. The results are also extended on the problems of asymptotically minimax statistical inference about a value of functional.