Abstract
For the statistical analysis of many geoscience data, incompleteness of data — either truncated and/or randomly censored, causes much difficulty. The first step toward analysing such data is to estimate the distribution and quantile functions, and to infer about the distribution and quantile functions by constructing the confidence bands for the functions from the truncated and/or censored observations. We not only introduce the methodologies but also apply them to geoscience data as illustration.
Geological Survey of Canada Contribution Number 23787
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References
Aly, E.-E., Csörgö, M. and Horváth, L. (1985) Strong Approximations of the quantile process of the product-limit estimator. Journal Multivariate Analysis, V. 16, N. 2, p.185–210.
Anderson, T.W. (1960). A modification of the sequential probability ratio test to reduce the sample size. Annals of Mathematical Statistics, V. 31, p.165–197.
Barr, D.R. and Davidson, T. (1973). A Kolomogorov-Smirnov test for censored samples. Technometrics V. 15, N. 4, p.737–757.
Breslow, N. and Crowley, J. (1974). A large sample study of the life table and product limit estimates under random censorship. Annals of Statistics, V. 2, p.437–453.
Burke, M.D., Csörgö, S. and Horváth, L. (1981). Strong approximations of some biometric estimates under random censorship. Z. Wahrsch. Verw. Gebiete 56, p.87–112.
Burke, M.D., Csörgö, S. and Horváth, L. (1986). An improved approximation rate for the product-limit process. Technical Report No.79, Carleton Univ., p.26–35.
Chung, C.F. (1986). Formulae for probabilities associated with Wiener and Brownian bridge processes. Technical Report No.79, Carleton Univ..
Chung, C.F. (1987a). WIENER PACK - A subroutine package for computing probabilities associated with Wiener and Brownian bridge processes. Geological Survey of Canada Paper 87-xx, in Press.
Chung, C.F. (1987b). An extenstion of the Kolmogorov-Smirnov confidence band for the distribution function on truncated data. To appear.
Chung, C.F. (1987c). FORTRAN 77 program for constructing and plotting confidence bands for the distribution and quantile functions for truncated data. Computer and Geosciences, Special Issue for NATO ASI on “Statistical Treatment for Estimation of Mineral and Energy Resources”.
Chung, C.F. (1987d). FORTRAN 77 program for constructing and plotting confidence bands for the distribution and quantile functions for randomly censored data. Computer and Geosciences, Special Issue for NATO ASI on “Statistical Treatment for Estimation of Mineral and Energy Resources”.
Chung, C.F., Csorgo, M., and Horvath, L. (1986). Confidence bands for quantile function under random censorship. To appear.
Csörgö, M. (1983). Quantile Processes with Statistical Applications. SIAM CBMS-NSF No. 42, 156p.
Csörgö, M. and Revesz, P. (1978). Strong approximations of the quantile process. Annals of Statistics, V. 4, p.882–894.
Csörgö, M. and Revesz, P. (1981). Strong Approximations in Probability and Statistics. Academic Press, 284p.
Csörgö, M. and Révész, P. (1984). Two approaches to constructing simultaneous confidence bounds for quantiles. Probability and Mathematical Statistics (Warsaw/Wroclaw) 4, p.221–236.
Csörgö, S. and Horváth L. (1985). Confidence bands from censored samples. Technical Report No. 44, Carleton University, p.39–76.
Donsker, M. (1952). Justification and extension of Doob’s hueristic approach to the Kolmogorov-Smirnov theorems. Annals of Mathematical Statistics, V.23, p.277–281.
Doob, J.L. (1949). A heuristic approach to the Kolmogorov-Smirnov theorems. Annals of Mathematical Statistics, V. 20, p.393–403.
Efron, B. (1967). The two-sample problem with censored data. In Proceedings of Fifth Berkeley Symposium in Mathematical Statistics and Probability, V. 4, p.831–853.
Gillespie, M.J. and Fisher, L. (1979). Confidence bands for the Kaplan-Meier survival curve estimate. Annals of Statistics, V. 7, N. 4, p.920–924.
Goodfellow, W.D. (1981). Regional stream sediment and water geochemistry reconnaissance data, Yukon and Northwest Territories; Geolocal Survey of Canada Open file 868, NTS 1051.
Hall, W.J. and Wellner J.A. (1980). Confidence bands for a survival curve from censored data. Biometrika V. 67, N. l, p.133–143.
IMSL (1984). IMSL Library – User’s Manual V. l-4.
Kaplan, E.L. and Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of American Statistical Association, V.53, p.457–481.
Komlós, J., Major, P. and Tusnady, G. (1975). Weak convergence and embedding. In Limit Theorems of Probability Theory (P. Révész ed.), p.149–165.
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 V. 17, p.507–510.
Nair, V.J. (1984). Confidence bands for survival functions with censored data: A comparative study. Technometrics V. 26, N.3, p.265–275
Stone, D., Kamineni, D.C. and Brown, A. (1984). Geology and fracture characteristics of the Underground Research Laboratory lease near Lac du Bonnet, Manitoba. T.R. 243, Atomic Energy of Canada Ltd Research Co..
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© 1988 D. Reidel Publishing Company, Dordrecht, Holland
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Chung, CJ.F. (1988). Confidence Bands for the Distribution and Quantile Functions for Truncated and Randomly Censored Data. In: Chung, C.F., Fabbri, A.G., Sinding-Larsen, R. (eds) Quantitative Analysis of Mineral and Energy Resources. NATO ASI Series, vol 223. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4029-1_26
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DOI: https://doi.org/10.1007/978-94-009-4029-1_26
Publisher Name: Springer, Dordrecht
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