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June, 1985 Demographic Incidence Rates and Estimation of Intensities with Incomplete Information
Ornulf Borgan, Henrik Ramlau-Hansen
Ann. Statist. 13(2): 564-582 (June, 1985). DOI: 10.1214/aos/1176349539

Abstract

Many population processes in demography, epidemiology and other fields can be represented by a time-continuous Markov chain model with a finite state space. If we have complete information on the life history of a cohort, the intensities of the Markov model may be estimated by the occurrence/exposure rates or by nonparametric techniques. In many situations, however, we have only incomplete information. In this paper we consider the special, but important, case where the occurrences and the total exposure are known, but not the distribution of the latter over the various separate statuses. Methods for handling such data, so-called demographic incidence rates, and methods for estimating the intensities from this kind of data, are known in the literature. However, their statistical properties are only vaguely known. The present paper gives a thorough presentation of the theory of these methods, and provide rigorous proofs of their statistical properties using stochastic process theory.

Citation

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Ornulf Borgan. Henrik Ramlau-Hansen. "Demographic Incidence Rates and Estimation of Intensities with Incomplete Information." Ann. Statist. 13 (2) 564 - 582, June, 1985. https://doi.org/10.1214/aos/1176349539

Information

Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0581.62070
MathSciNet: MR790557
Digital Object Identifier: 10.1214/aos/1176349539

Subjects:
Primary: 62M05
Secondary: 62P99

Keywords: Asymptotic theory , cohort analysis , counting processes , cumulative incidence rates , Martingales , occurrence/exposure rates , time-continuous Markov chains

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 2 • June, 1985
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