Sankhya: The Indian Journal of Statistics1993, Volume 55, Series A, Pt. 1, 49-65
SOLUTION OF AN OPTIMIZATION PROBLEM ARISING IN MAXIMUM LIKELIHOOD ESTIMATION OF ORDERED DISTRIBUTIONS
J. C. PARNAMI, HARSHINDER SINGH, Punjab university
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.
This article in Mathematical Reviews.