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\noindent Statistica Sinica {\bf 16}(2006), 93-119

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\centerline{\large\bf ESTIMATION IN A SEMIPARAMETRIC }
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\centerline{\large\bf MODULATED RENEWAL PROCESS}
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\author{Dorota M. Dabrowska and Wai Tung Ho}
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\centerline{\it University of California, Los Angeles and SPSS Inc.} %, Chicago}
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\begin{quotation}
\noindent {\it Abstract:}
We consider parameter estimation
in a regression model corresponding to  an i.i.d.~sequence
of censored observations of a
finite state modulated renewal process. The model assumes a
similar form as in  Cox regression except that the baseline
intensities  are functions of the backwards recurrence time
of the
process and a time dependent covariate. As a result of this
it falls outside the class of multiplicative intensity
counting process models. We use kernel estimation to construct
estimates of the regression coefficients and baseline cumulative
hazards. We give conditions for
consistency and asymptotic normality of estimates. Data from
a bone marrow transplant study are used to illustrate the results.\par
\vspace{9pt}
\noindent {\it Key words and phrases:}
Modulated renewal process, kernel estimation, U processes.\par
\end{quotation}

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