On Asymptotically Optimal Sequential Bayes Interval Estimation Procedures

Gleser, Leon Jay ; Kunte, Sudhakar

Ann. Statist., Tome 4 (1976) no. 1, p. 685-711 / Harvested from Project Euclid

Résumé

A theory of sequential Bayes interval estimation procedures for a single parameter is developed for the case where the loss for using an interval $I$ is a linear combination of the length of $I$, the indicator of noncoverage of $I$, and the number of observations taken. A class of stopping rules $\{t(c): c > 0\}$ is shown to be asymptotically pointwise optimal (A.P.O.) and asymptotically optimal (A.O.) for the confidence interval problem as the cost $c$ per observation tends to 0. The results require generalization of Bickel and Yahav's (1968) general conditions for the existence of A.P.O. and A.O. stopping rules to the case where the terminal risk $Y_n$ satisfies $f(n)Y_n \rightarrow V$ for $f(n)$ a regularly varying function on the integers.

Détail

Publié le : 1976-07-14
Classification:  Bayes interval estimation procedures,  sequential inference,  stopping rules,  asymptotically pointwise optimal,  asymptotically optimal,  moderate deviation theory,  regularly varying function,  62L12,  62L15,  62F15,  60G40,  62F10,  62F25,  60F99