Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 3, pp. 486--499
ESTIMATING THE NUMBER OF COMPONENTS OF A SYSTEM OF SUPERIMPOSED RENEWAL PROCESS
ANUP DEWANJI, Indian Statistical Institute
TAPAN K. NAYAK, George Washington University
PRANAB K. SEN, University of North Carolina
SUMMARY. Consider a superposition of an unknown number, $\nu$, of independent, identically distributed renewal processes and supose that whenever an event occurs, the component process in which it occurred can be identified. We discuss maximum likelihood estimation of $\nu$ and the parameters of the common renewal density based on the data generated over a fixed interval of time. Some asymptotic properties of these methods are discussed. In particular, we prove asymptotic normality of a class of estimators under quite general conditions.
AMS (1991) subject classification. 62M09, 62F12.
Key words and phrases. Renewal process, marked point process, consistency, maximum likelihood.
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