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September, 1990 Goodness of Fit Tests in Models for Life History Data Based on Cumulative Hazard Rates
Nils Lid Hjort
Ann. Statist. 18(3): 1221-1258 (September, 1990). DOI: 10.1214/aos/1176347748

Abstract

To check the validity of an assumed parametric model for survival data, one may compare $\hat{A}(t)$, the nonparametric Nelson-Aalen plot of the cumulative hazard rate, with $A(t, \hat{\theta})$, the estimated parametric cumulative hazard rate, $\hat{\theta}$ being for example the maximum likelihood estimator. Convergence in distribution of $\sqrt n (\hat{A}(t) - A(t, \hat{\theta}))$ and more general processes is studied in the present paper, employing the general framework of counting processes, which allows for quite general models for life history data and for quite general censoring schemes. The results are applied to the construction of $\chi^2$-type statistics for goodness of fit. Cramer-von Mises and Kolmogorov-Smirnov type tests are presented in the case where the unknown parameter is one-dimensional. Power considerations are also included, and some optimality results are reached. Finally tests are constructed for the hypothesis that the unspecified hazard rate part in Cox's regression model follows a parametric form.

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Nils Lid Hjort. "Goodness of Fit Tests in Models for Life History Data Based on Cumulative Hazard Rates." Ann. Statist. 18 (3) 1221 - 1258, September, 1990. https://doi.org/10.1214/aos/1176347748

Information

Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0714.62037
MathSciNet: MR1062707
Digital Object Identifier: 10.1214/aos/1176347748

Subjects:
Primary: 62G10
Secondary: 60B10

Keywords: Censoring , chi squared statistics , counting processes , goodness of fit , hazard rates , local power , weak convergence

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 3 • September, 1990
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