Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 1, 49-65

SOLUTION OF AN OPTIMIZATION PROBLEM ARISING IN MAXIMUM LIKELIHOOD ESTIMATION OF ORDERED DISTRIBUTIONS

By

J. C. PARNAMI, HARSHINDER SINGH, *Punjab university*

And

PREM S. PURI, *Purdue University *

SUMMARY. We propose and solve an optimizatin problem arising in maximum likelihood estimation of ordered distributions. In particular it generalizes a recent result due to Puri and Singh (1988). As an application of our results we obtain a "maximum likelihood" estimate *F^*_{n} of a cumulative distribution function (c. d. f) *F*, based on a sample of size *n *from *F*, where *F* is known to satisfy *F*_{1}(x) £
*F*(x) £
*F*_{2}(x), "
x, for two given c.d.f s *F*_{1} and *F*_{2}. It is also shown that *F^*_{n} is strongly consistent._{ }

*AMS (1989) subject classification.* 62G05

*Key words and phrases*. Statistical inference under order restrictions, maximum likelihood estimation, isotonic regression, stochastically ordered distributions.

This article in Mathematical Reviews.