The Annals of Statistics

Estimation in some Counting Process Models with Multiplicative Structure

Ake Svensson

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Abstract

It is assumed that we observe one realization of an $r$-dimensional counting process with intensities that are products of a predictable weight process, a common function of time and parameters $\beta_i, i = 1, \cdots, r$, which distinguish the components. Provided the realization observed brings increasing information on $\beta$ as the observed time grows, strong consistency of a partial ML estimator is proved. For such realizations it is also proved that the estimate, after applying a random normalization, is asymptotically standard normal.

Article information

Source
Ann. Statist., Volume 17, Number 4 (1989), 1501-1508.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347378

Digital Object Identifier
doi:10.1214/aos/1176347378

Mathematical Reviews number (MathSciNet)
MR1026296

Zentralblatt MATH identifier
0695.62208

JSTOR
links.jstor.org

Subjects
Primary: 62M09: Non-Markovian processes: estimation

Keywords
Counting processes Cox regression model martingale limit theorems

Citation

Svensson, Ake. Estimation in some Counting Process Models with Multiplicative Structure. Ann. Statist. 17 (1989), no. 4, 1501--1508. doi:10.1214/aos/1176347378. https://projecteuclid.org/euclid.aos/1176347378


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