**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series A, Pt. 1, pp. 88--99

**CONSISTENCY OF THE MLE FOR A GENERAL SEQUENTIAL DESIGN PROBLEM**

By

SOMNATH DATTA, *University of Georgia*

SUMMARY. A simple proof of consistency of a maximum likelihood estimator in a general sequential design problem is obtained by a uniform L_{1} law of large numbers for martingales. A number of examples satisfying the (sufficient) conditions of our theorems are provided.

*AMS (1990) subject classification.* 62F12, 62F10.

*Key words and phrases.* Sequential design, maximum likelihood, consistency.