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Goodness-of-fit testing in interval censoring case 1. (English) Zbl 1090.62044
Summary: In the interval censoring case 1, an event occurrence time is unobservable, but one observes an inspection time and whether the event has occurred prior to this time or not. The focus here is to provide tests of goodness-of-fit hypotheses pertaining to the distribution of the event occurrence time. The proposed tests are based on certain marked empirical processes for testing a simple hypothesis and the Stute-Thies-Zhu transformation [W. Stute, S. Thies and L.-X. Zhu, Ann. Stat. 26, No. 5, 1916–1934 (1998; Zbl 0930.62044)] of such a process for fitting a parametric family of distributions. These tests are asymptotically distribution-free, consistent against a large class of fixed alternatives and have nontrivial asymptotic power against a large class of local alternatives. A simulation study is included to exhibit the finite sample level preservation and power behavior.

MSC:
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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[1] An, H.-Z., Cheng, B., 1991. A Kolmogorov-Smirnov type statistic with application to test for nonlinearity in time series. Int. Statist. Rev., 59, 287-307. · Zbl 0748.62049
[2] Billingsley, P., Convergence of probability measures, (1968), Wiley New York · Zbl 0172.21201
[3] Buckley, M.J., Detecting a smooth signal: optimality of cusum based procedures, Biometrika, 78, 253-262, (1991)
[4] Diamond, I.D.; McDonald, J.W., Analysis of current status data, (), 231-252
[5] Diamond, I.D.; McDonald, J.W.; Shah, I.H., Proportional hazards models for current status data: application to the study of differentials in age at weaning in pakistan, Demography, 23, 607-620, (1986)
[6] Finkelstein, D.M., A proportional hazards model for interval-censored failure time data, Biometrics, 42, 845-854, (1986) · Zbl 0618.62097
[7] Finkelstein, D.M.; Wolfe, R.A., A semiparametric model for regression analysis of interval-censored failure time data, Biometrics, 41, 933-945, (1985) · Zbl 0655.62101
[8] Groeneboom, P., Wellner, J.A., 1992. Information Bounds and Nonparametric Maximum Likelihood Estimation. DMV Seminar, vol. 19. Birkhauser Verlag, Basel, viii+126pp. · Zbl 0757.62017
[9] Hoel, D.G.; Walburg, H.E., Statistical analysis of survival experiment, J. national cancer inst., 49, 361-372, (1972)
[10] Huber, P.J., 1981. Robust Statistics. Wiley Series in Probability and Mathematical Statistics, Wiley, New York. · Zbl 0536.62025
[11] Jewell, N.P., van der Laan, M., 2004. Current status data: review, recent developments and open problems. Advances in Survival Analysis. Handbook of Statistics, vol. 23, Elsevier, Amsterdam, pp. 625-642.
[12] Keiding, N., Age-specific incidence and prevalence: a statistical perspective (with discussion), J. roy. statist. soc. ser. A, 154, 371-412, (1991) · Zbl 1002.62504
[13] Liese, F.; Vajda, I., A general asymptotic theory of M-estimators. II, Math. methods statist., 13, 1, 82-95, (2004) · Zbl 1185.62053
[14] von Neumann, J., Distribution of the ratio of the Mean square successive difference to the variance, Ann. math. statist., 12, 367-395, (1941) · Zbl 0060.29911
[15] Stute, W., Nonparametric model checks for regression, Ann. statist., 25, 613-641, (1997) · Zbl 0926.62035
[16] Stute, W.; Thies, S.; Zhu, L.-X., Model checks for regression: an innovation process approach, Ann. statist., 26, 1916-1934, (1998) · Zbl 0930.62044
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