On the asymptotic non-null distribution of randomly stopped log- likelihood ratio statistic. (English) Zbl 0769.62016

Basu, A. K.; Bhattacharya, Debasis

Bull., Calcutta Stat. Assoc. 42, No. 167-168, 255-260 (1992).

Summary: The non-null asymptotic distribution of a randomly stopped log-likelihood ratio statistic for general dependent processes has been obtained. We observed that under certain regularity conditions the limiting distribution of randomly stopped log-likelihood ratio statistic under alternative hypothesis is again a mixture of normal distributions. Some possible applications of the result have also been pointed out.

MSC:

62E20	Asymptotic distribution theory in statistics
62L10	Sequential statistical analysis
60F05	Central limit and other weak theorems

Keywords:

non-null asymptotic distribution; randomly stopped log-likelihood ratio statistic; general dependent processes; mixture of normal distributions