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

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