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Confidence bands for quantile function under random censorship

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Abstract

Some new confidence bands are established for the quantile function from randomly censored data. The method does not require estimation of the density function. As an application, we construct bands for the quantile function of the length of fractures in the granitic plutons near Lac du Bonnet, Manitoba, where an Underground Research Laboratory is being built for the nuclear waste disposal program in Canada.

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References

  • Aalen, O. (1976). Nonparametric inference in connection with multiple decrement models, Scand. J. Statist., 3, 15–27.

    Google Scholar 

  • Alexander, C. H. (1980). Simultaneous confidence bounds for the tail of an inverse distribution, Ann. Statist., 8, 1391–1394.

    Google Scholar 

  • Alexander, C. H. (1982). Simultaneous confidence bounds, Ann. Statist., 10, 321.

    Google Scholar 

  • Aly, E-E. A. A., Csörgő, M. and Horváth, L. (1985). Strong approximations of the quantile process of the product-limit estimator, J. Multivariate Anal., 16, 185–210.

    Google Scholar 

  • Anderson, T. W. (1960). A modification of the sequential probability ratio test to reduce the sample size, Ann. Math. Statist., 31, 165–197.

    Google Scholar 

  • Breslow, N. and Crowley, J. (1974). A large sample study of the life table and product limit estimates under random censorship, Ann. Statist., 2, 437–453.

    Google Scholar 

  • Burke, M. D., Csörgő, S. and Horváth, L. (1981). Strong approximation of some biometric estimates under random censorship, Z. Wahrsch. Verw. Gebiete, 56, 87–112.

    Google Scholar 

  • Burke, M. D., Csörgő, S. and Horváth, L. (1988). A correction to and improvement of “Strong approximations of some geometric estimates under random censorship”, Probab. Theory Related Fields, 79, 51–57.

    Google Scholar 

  • Chung, C-J. F. (1986). Formulae for probabilities associated with Wiener and Brownian bridge processes, Tech. Rep. Ser. Lab. Res. Stat. Probab., No. 79, Carleton University, Ottawa.

    Google Scholar 

  • Chung, C-J. F. (1987). Wiener pack—A subroutine package for computing probabilities associated with Wiener and Brownian bridge processes, Geol. Surv., Canada Paper, 87–12.

  • Csörgő, M. (1983). Quantile Processes with Statistical Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, 42, SIAM, Philadelphia, Pennsylvania.

    Google Scholar 

  • Csörgő, M. and Révész, P. (1981). Strong Approximations in Probability and Statistics, Academic Press, New York.

    Google Scholar 

  • Csörgő, M. and Révész, P. (1984). Two approaches to constructing simultaneous confidence bounds for quantiles, Probab. Math. Statist. (Warsaw/Wroclaw), 4, 221–236.

    Google Scholar 

  • Csörgő, S. and Horváth, L. (1983). The baboons come down from the trees quite normally, Probability and Statistical Inference, Proc. 4th Pannonian Symp. Math. Statist., (eds. W., Grossman, F., Konecny, G., Pflug and W., Wertz), 95–106, Reidel, Dordrecht.

    Google Scholar 

  • Csörgő, S. and Horváth, L. (1986). Confidence bands from censored samples, Canad. J. Statist., 14, 131–144.

    Google Scholar 

  • Efron, B. (1967). The two-sample problem with censored data, Proc. fifth Berkeley Symp. on Math. Statist. Prob., Vol. 4, 831–853.

    Google Scholar 

  • Feller, W. (1966). An Introduction to Probability Theory and Its Applications, Wiley, New York.

    Google Scholar 

  • Gill, R. D. (1980). Censoring and stochastic integrals, Mathematical Centre Tracts, 124, Amsterdam.

  • Gill, R. D. (1983). Large sample behaviour of the product limit estimator on the whole line, Ann. Statist., 11, 49–58.

    Google Scholar 

  • Gillespie, M. J. and Fisher, L. (1979). Confidence bands for the Kaplan-Meier survival curve estimate, Ann. Statist., 7, 920–924.

    Google Scholar 

  • Hall, J. W. and Wellner, J. A. (1980). Confidence bands for a survival curve from censored data, Biometrika, 67, 133–143.

    Google Scholar 

  • Kaplan, E. L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc., 53, 457–481.

    Google Scholar 

  • Koziol, J. A. and Byar, D. P. (1975). Percentage points of the asymptotic distributions of one and two sample K-S statistics for truncated or censored data, Technometrics, 17, 507–510.

    Google Scholar 

  • Lo, S. H. and Singh, K. (1986). The product limit estimator and the bootstrap: Some asymptotic representations, Probab. Theory Related Fields, 71, 455–465.

    Google Scholar 

  • Nair, V. N. (1981). Plots and tests for goodness of fit with randomly censored data, Biometrika, 68, 99–103.

    Google Scholar 

  • Nair, V. N. (1982). Goodness of fit tests for multiply right censored data, Nonparametric Statistical Inference, (eds. B. V., Gnedenko, M. L., Puri and I., Vincze), 653–666, North-Holland, Amsterdam.

    Google Scholar 

  • Nair, V. N. (1984). Confidence bands for survival functions with censored data, A comparative study, Technometrics, 26, 265–275.

    Google Scholar 

  • Sander, J. M. (1975). The weak convergence of quantiles of the product-limit estimator, Tech. Report No. 5, Stanford University.

  • Stone, D., Kamineni, D. C. and Brown, A. (1984). Geology and fracture characteristics of the Underground Research Laboratory lease near Lac du Bonnet, Manitoba, Tech. Report-243, Atomic Energy of Canada Limited Research Company.

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Additional information

Geological Survey of Canada Contribution Number 10386.

Research partially supported by an NSERC Canada Grant.

Research done while at Carieton University, supported by NSERC Canada and EMR Canada Grants of M. Csörgő.

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Chung, CJ.F., Csörgő, M. & Horváth, L. Confidence bands for quantile function under random censorship. Ann Inst Stat Math 42, 21–36 (1990). https://doi.org/10.1007/BF00050776

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  • DOI: https://doi.org/10.1007/BF00050776

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