Communications for Statistical Applications and Methods

  • 제26권5호
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  • Pages.431-443
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  • 2019
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Tests based on EDF statistics for randomly censored normal distributions when parameters are unknown

  • 투고 : 2019.02.03
  • 심사 : 2019.08.26
  • 발행 : 2019.09.30
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초록

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

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참고문헌

  1. Bagdonavicius V, Kruopis J, and Nikulin MS (2011). Non-Parametric Tests for Complete Data, John Wiley & Sons, New Jersey.
  2. Breslow N and Crowley J (1974). A large sample study of the life table and product limit estimates under random censorships, The Annals of Statistics, 2, 437-453. https://doi.org/10.1214/aos/1176342705
  3. Chen C (1984). A correlation goodness-of-fit test for randomly censored data, Biometrika, 71, 315-322. https://doi.org/10.1093/biomet/71.2.315
  4. Chen YY, Hollander M, and Langberg NA (1982). Small-sample results for the Kaplan Meier estimator, Journal of the American statistical Association, 77, 141-144. https://doi.org/10.1080/01621459.1982.10477777
  5. Csorgo S and Horvath L (1981). On the Koziol-Green Model for random censorship, Biometrika, 68, 391-401. https://doi.org/10.1093/biomet/68.2.391
  6. D'Agostino RB (1986). Test for the normal distribution. In D'Agostino RB and Stephens MA (Eds), Goodness-of-Fit Techniques (Chapter 9), Marcel Dekker, New York.
  7. Efron B (1967). The two sample problem with censored data. In Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, 4, 831-853.
  8. Freireich EJ, Gehan EA, Frei E, et al. (1963). The effect of 6-mercaptopurine on the duration of steroid-induced remissions in acute leukemia: a model for evaluation of other potential useful therapy, Blood, 21, 699-716. https://doi.org/10.1182/blood.V21.6.699.699
  9. Kaplan EL and Meier P (1958). Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452
  10. Kim N (2011). Testing log normality for randomly censored data, The Korean Journal of Applied Statistics, 24, 883-891. https://doi.org/10.5351/KJAS.2011.24.5.883
  11. Kim N (2012). Testing exponentiality based on EDF statistics for randomly censored data when the scale parameter is unknown, The Korean Journal of Applied Statistics, 25, 311-319. https://doi.org/10.5351/KJAS.2012.25.2.311
  12. Kim N (2017). Goodness-of-fit tests for randomly censored Weibull distributions with estimated parameters, Communications for Statistical Applications and Methods, 24, 519-531. https://doi.org/10.5351/CSAM.2017.24.5.519
  13. Kim N (2018). On the maximum likelihood estimation for a normal distribution under random censoring, Communications for Statistical Applications and Methods, 25, 647-658. https://doi.org/10.29220/CSAM.2018.25.6.647
  14. Kleinbaum DG and Klein M (2005). Survival Analysis: A Self-Learning Test, Springer, New York.
  15. Koziol JA (1980). Goodness-of-fit tests for randomly censored data, Biometrika, 67, 693-696. https://doi.org/10.1093/biomet/67.3.693
  16. Koziol JA and Green SB (1976). A Cramer-von Mises statistic for randomly censored data, Biometrika, 63, 465-474. https://doi.org/10.1093/biomet/63.3.465
  17. Lee ET and Wang JW (2003). Statistical Methods for Survival Data Analysis, John Wiley & Sons, New Jersey.
  18. Meier P (1975). Estimation of a distribution function from incomplete observations. In J. Gani (Ed), Perspectives in Probability and Statistics, Academic Press, London.
  19. Michael JR and Schucany WR (1986). Analysis of data from censored samples. In D'Agostino RB and Stephens MA (Eds), Goodness of Fit Techniques (Chapter 11), Marcel Dekker, New York.
  20. Nair VN (1981). Plots and tests for goodness of fit with randomly censored data, Biometrika, 68, 99-103. https://doi.org/10.1093/biomet/68.1.99
  21. Stephens MA (1986). Tests based on EDF statistics. In D'Agostino RB and Stephens MA (Eds), Goodness-of-Fit Techniques (Chapter 4), Marcel Dekker, New York.
  22. Tableman M and Kim JS (2004). Survival Analysis using S: Analysis of Time-to-Event Data, Champman & Hall CRC, Florida.
  23. Thode HC (2002). Testing for Normality, Marcel Dekker, New York.