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 F1(x) £ F(x) £ F2(x), " x, for two given c.d.f s F1 and F2. 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.

FULL PAPER.

This article in Mathematical Reviews.