Exact Kolmogorov-type tests for left-truncated and/or right-censored data

Journal of the American Statistical Association

Volumn 83, Issue 401, 1988, Pages 213-221

  Guilbaud, Olivier ^a  

^a Peptide Hormones   (Sweden)

Author keywords

General validity; Product limit estimator; Small sample test; Survival analysis

Indexed keywords

EID: 0040484379     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1988.10478589     Document Type: Article

References (33)

1. Aalen, O. O. (1976), “Nonparametric Inference in Connection With Multiple Decrement Models,” Scandinavian Journal of Statistics, 3, 15–27.
2. Andersen, P. K., and Borgan, Ø. (1985), “Counting Process Models for Life History Data: A Review” (with discussion), Scandinavian Journal of Statistics, 12, 97–158.
3. Breslow, N. E., and Crowley, J. (1974), “A Large Sample Study of the Life Table and Product Limit Estimates Under Random Censorship,” The Annals of Statistics, 2, 437–453.
4. Burke, M. D., Csörgő, S., and Horváth, L. (1981), “Strong Approximations of Some Biometrie Estimates Under Random Censorship,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 56, 87–112.
5. Cox, D. R., and Oakes, D. (1984), Analysis of Survival Data, London: Chapman & Hall.
6. Csörgö, S., and Horváth, L. (1986), “Confidence Bands for Censored Samples,” Canadian Journal of Statistics, 14, 131–144.
7. Dahlquist, G., and Björck, Å. (1974), Numerical Methods (trans. N. Anderson), Englewood Cliffs, NJ: Prentice-Hall.
8. Daniels, H. E. (1945), “The Statistical Theory of the Strength of Bundles of Threads: I,” Proceedings of the Royal Society, Ser. A, 183, 405–435.
9. Durbin, J. (1971), “Boundary-Crossing Probabilities for the Brownian Motion and Poisson Processes and Techniques for Computing the Power of the Kolmogorov-Smirnov Test,” Journal of Applied Probability, 8, 431–453.
10. —— (1973), Distribution Theory for Tests Based on the Sample Distribution Function, Philadelphia: Society for Industrial and Applied Mathematics.
11. Fleming, T. R., O’Fallon, J. R., O’Brien, P. C., and Harrington, D. P. (1980), “Modified Kolmogorov-Smirnov Test Procedures With Application to Arbitrarily Right-Censored Data,” Biometrics, 36, 607–625.
12. Freireich, E. J., et al. (1963), “The Effect of 6-Mercaptopurine on the Duration of Steroid-Induced Remissions in Acute Leukemia,” Blood, 21, 699–716.
13. Gill, R. (1983), “Large Sample Behaviour of the Product-Limit Estimator on the Whole Line,” The Annals of Statistics, 11, 49–58.
14. Gillespie, M. J., and Fisher, L. (1979), “Confidence Bands for the Kaplan-Meier Survival Curve Estimate,” The Annals of Statistics, 7, 920–924.
15. Gleser, L. J. (1985), “Exact Power of Goodness-of-Fit Tests of Kolmogorov Type for Discontinuous Distributions,” Journal of the American Statistical Association, 80, 954–958.
16. Guilbaud, O. (1986a), “Stochastic Inequalities for Kolmogorov and Similar Statistics, With Confidence Region Applications,” Scandinavian Journal of Statistics, 13, 301–305.
17. —— (1986b), “Exact Compensations for Left Truncation and/or Right Censorship in Kolmogorov Type Tests,” Research Report 1986:7, University of Stockholm, Dept. of Statistics.
18. Hall, W. J., and Wellner, J. A. (1980), “Confidence Bands for a Survival Curve From Censored Data,” Biometrika, 67, 133–143.
19. Hyde, J. (1977), “Testing Survival Under Right Censoring and Left Truncation,” Biometrika, 64, 225–230.
20. Kaplan, E. L., and Meier, P. (1958), “Nonparametric Estimation From Incomplete Observations,” Journal of the American Statistical Association, 53, 457–481.
21. Karlin, S., and Taylor, H. M. (1981), A Second Course in Stochastic Processes, New York: Academic Press.
22. Kolmogorov, A. N. (1933), “Sulla Determinazione Empírica di una Legge di Distribuzione,” Giornale Dell’lstituto Italiano Degli Attuari, 4, 8391.
23. —— (1941), “Confidence Limits for an Unknown Distribution Function,” Annals of Mathematical Statistics, 12, 461–463.
24. Lehmann, E. L. (1986), Testing Statistical Hypotheses (2nd ed.), New York: John Wiley.
25. Meier, P. (1976), “Estimation of a Distribution Function From Incomplete Observations,” in Perspectives in Probability and Statistics, ed. J. Gani, New York: Academic Press, pp. 67–88.
26. Miller, R. G., Jr. (1981), Survival Analysis, New York: John Wiley.
27. Nair, V. N. (1984), “Confidence Bands for Survival Functions with Censored Data: A Comparative Study,” Technometrics, 26, 265–275.
28. Niederhausen, H. (1981), “Scheffer Polynomials for Computing Exact Kolmogorov-Smirnov and Rényi Type Distributions,” The Annals of Statistics, 9, 923–944.
29. Noether, G. E. (1963), “Note on the Kolmogorov Statistic in the Discrete Case,” Metrika, 7, 115–116.
30. Peterson, A. V., Jr. (1983), “Kaplan-Meier Estimator,” in Encyclopedia of Statistical Sciences (Vol. 4), eds. S. Kotz and N. A. Johnson, New York: John Wiley
31. Pratt, J. W. (1983), “Significance Levels, Confidence Levels, Closed Models, and Discrete Distributions,” in Recent Advances in Statistics, eds. H. Rizvi, J. S. Rustavi, and D. Siegmund, New York: Academic Press, pp. 601–611.
32. Smirnov, N. V. (1939), “Sur les Ecart de la Courbe de Distribution Empirique,” Matematiceskii Sbornik, 6, 3–26.
33. Walsh, J. E. (1963), “Bounded Probability Properties of the Kolmogorov-Smirnov and Similar Statistics for Discrete Data,” Annals of the Institute of Statistical Mathematics, 15, 153–158.