Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 3, 392-407

ISOTONIC MAXIMUM LIKELIHOOD ESTIMATION FOR THE CHANGE POINT OF A HAZARD RATE

By

S. N. JOSHI, *Indian Statistical Institute, Bangalore*

And

STEVEN N. MACEACHERN, *The Ohio State University, Ohio
*

SUMMARY. A hazard rate $\lambda(t)$ is assumed to be of the shape of the ``first'' part of a ``bathtub'' model, i.e., \lambda(t)$ is non-increasing for $t<\tau$ and is constant for $t\geq\tau$. The isotonic maximum likelihood estimator of the hazard rate is obtained and its asymptotic distribution is investigated. This leads to the maximum likelihood estimator and a confidence interval for a new version of the change point parameter. Their asymptotic properties are investigated. Some simulations are reported.

*AMS (1991) subject classification.* 62G05, 62N05, 62G07

*Key words and phrases*. Isotonic model, failure rate, change point, asymptotic distribution, hypothesis testing, confidence interval