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Nonparametric likelihood ratio goodness-of-fit tests for survival data

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  • Li, Gang

Abstract

Berk and Jones (Z. Wahrsch. Verw. Gebiete 47 (1979) 47) described a nonparametric likelihood test of uniformity that is more efficient, in Bahadur's sense, than any weighted Kolmogorov-Smirnov test at any alternative. This article shows how to obtain a nonparametric likelihood test of a general parametric family for incomplete survival data. A nonparametric likelihood ratio test process is employed to measure the discrepancy between a parametric family and the observed data. Large sample properties of the likelihood ratio test process are studied under both the null and alternative hypotheses. A Monte Carlo simulation method is proposed to estimate its null distribution. We show how to produce a likelihood ratio graphical check as well as a formal test of a parametric family based on the developed theory. Our method is developed for the right-censorship model, but can be easily extended to some other survival models. Illustrations are given using both real and simulated data.

Suggested Citation

  • Li, Gang, 2003. "Nonparametric likelihood ratio goodness-of-fit tests for survival data," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 166-182, July.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:1:p:166-182
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    References listed on IDEAS

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    1. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    2. Li, Gang, 1995. "On nonparametric likelihood ratio estimation of survival probabilities for censored data," Statistics & Probability Letters, Elsevier, vol. 25(2), pages 95-104, November.
    3. Li, Gang & Sun, Yanqing, 2000. "A simulation-based goodness-of-fit test for survival data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 403-410, May.
    4. Vaart,A. W. van der, 1998. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521496032.
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    2. Koning, A.J. & Peng, L., 2005. "Goodness-of-fit tests for a heavy tailed distribution," Econometric Institute Research Papers EI 2005-44, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Pang, Wan-Kai & Hou, Shui-Hung & Yu, Wing-Tong, 2007. "On a proper way to select population failure distribution and a stochastic optimization method in parameter estimation," European Journal of Operational Research, Elsevier, vol. 177(1), pages 604-611, February.
    4. Sundarraman Subramanian, 2020. "Function-based hypothesis testing in censored two-sample location-scale models," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 183-213, January.

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