THE STRUCTURE OF THE ASSUMED MODEL THROUGH THE DISCRETIZED LIKELIHOOD ESTIMATOR

In the presence of a nuisance parameter the asymptotic deficiency of the discretizedlikelihood estimator (DLE) relative to the bias-adjusted maximum likelihood estimatoris obtained under the assumed model. It consists of two parts. One is the lossof information associated with the DLE of the parameter to be estimated. Another,is that due to the "incorrectness" of the assumed model. Some examples on the normaland Weibull type distributions are given

The clarification of the structure of the inverse problem in statisticsand its applications

科学研究費助成事業(科学研究費補助金)研究成果報告書：挑戦的萌芽研究2009-2011課題番号：2165006

統計的欠損性の階層構造の解明とその応用

科学研究費助成事業 研究成果報告書：挑戦的萌芽研究2015-2017課題番号 : 15K1199

AN INFORMATION INEQUALITY FOR THE BAYES RISK IN A FAMILY OF UNIFORM DISTRIBUTION

For a family of uniform distribution on the interval [8 - (1/2), e - (1/2)]\u27 the informationinequality for the bayes risk of any estimator of e is given under the quadratic Joss and the uniform priordistribution on an interval [-c,c]. The lower bound for the Bayes risk is shown to be sharp. And also thelower bound for the limit inferior of Bayes risk as c -jo 00 is seen to be attained by the mid-range estimator

A HIGHER ORDER LARGE-DEVIATION APPROXIMATION FOR THE DISCRETE DISTRIBUTIONS

For a sum of independent discrete random variables, its higher order large-deviation approximation is discussed. An approximation to the tail probability of the distribution of the sum is provided, and its numerical comparison with other approximations is done in the binomial case. Consequently, the approximation formula is seen to be more accurate