The Annals of Statistics

Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models

Odd Aalen

Full-text: Open access

Abstract

Nonparametric estimators are proposed for transition probabilities in partial Markov chains relative to multiple decrement models. The estimators are generalizations of the product limit estimator. We study the bias of the estimators, prove a strong consistency result and derive asymptotic normality of the estimators considered as stochastic processes. We also compute their efficiency relative to the maximum likelihood estimators in the case of constant forces of transition.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 534-545.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344198

Digital Object Identifier
doi:10.1214/aos/1176344198

Mathematical Reviews number (MathSciNet)
MR478510

Zentralblatt MATH identifier
0383.62057

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62M05: Markov processes: estimation 62E20: Asymptotic distribution theory 62G20: Asymptotic properties

Keywords
Multiple decrement model competing risks life table partial Markov chain partial transition probability Markov chain estimation product limit estimator non-parametric theory

Citation

Aalen, Odd. Nonparametric Estimation of Partial Transition Probabilities in Multiple Decrement Models. Ann. Statist. 6 (1978), no. 3, 534--545. doi:10.1214/aos/1176344198. https://projecteuclid.org/euclid.aos/1176344198


Export citation