Bøger af Masafumi Akahira

In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter.

However, there exists here a whole class of asymptotically efficient estimators which are thus asymptotically equivalent to the MLE. These are situations where the MLE or other estimators are not asymptotically normally distributed, or where l 2 their order of convergence (or consistency) is not n / , as in the regular cases.

In order to obtain many of the classical results in the theory of statistical estimation, it is usual to impose regularity conditions on the distributions under consideration.