TWO-SAMPLE TEST FOR RANDOMLY CENSORED DATA
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Abstract
In this paper, a nonparametric test has been proposed for the two-sample scale problem, when sample observations are randomly right censored. The proposed test is based on the extremes of observations as an extension of commonly used Gehan’s test for two-sample problem. Critical values are obtained through simulation for various lifetime distributions at different sample sizes. Power performance for the proposed test is studied considering various distributions. On comparing with the Gehan’s test, it is found that the proposed test has more statistical power and efficiency for some special cases. An illustration with real-life data set is also provided.
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Licensee MJS, Universiti Malaya, Malaysia. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
References
Alling D. (1963). Early decision in the Wilcoxon two-sample test. Journal of the American Statistical Association 58: 713-720.
Deshpande JV. & Purohit SG. (2015). Lifetime Data: Statistical Models and Methods (2nd edition), Singapore: World Scientific Publishing Co. Pvt. Ltd.
Efron B. (1967). The two-sample problem with censored data. Berkeley Symposium on Mathematical Statistics and Probability 5.4: 831-853.
Gehan EA. (1965). A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika 52, 202-223.
Goyal M. & Kumar N. (2020). Two new classes of nonparametric tests for scale parameters. Journal of Statistical Computation and Simulation 90: 3093-3105.
Halperin M. (1960). Extension of the Wilcoxon-Mann-Whitney test to samples censored at the same fixed point. Journal of the American Statistical Association 55: 125-138.
Kaplan EL. & Meier P. (1958). Non-Parametric estimation from incomplete observations. Journal of the American Statistical Association 53, 457-481.
Kössler W. (1994). Restrictive adaptive tests for the treatment of the two-sample scale problem. Computational Statistics & Data Analysis 18: 513–524.
Kössler W. & Kumar N. (2010). An adaptive test for the two-sample scale problem based on U-statistics. Communications in Statistics - Simulation and Computation 39: 1785-1802.
Lee ET., Desu MM. & Gehan EA. (1975). A Monte Carlo study of the power of some two-sample tests. Biometrika 62: 425-432.
Mantel N. (1967). Ranking procedures for arbitrarily restricted observation. Biometrics 23: 65-78.
Miller RG. (2011). Survival Analysis (2nd edition), New York, USA: John Wiley & Sons.
Mood AM. (1954). On the asymptotic efficiency of certain nonparametric two-sample tests. Annals of Mathematical Statistics 25: 514–522.
Rao UVR., Savage IR. & Sobel M. (1960). Contributions to the theory of rank order statistics: the two-sample censored case. Annals of Mathematical Statistics 31: 415-426.
Stablein DM. & Koutrouvelis IA. (1985). A two-sample test sensitive to crossing hazards in uncensored and singly censored data. Biometrics 41: 643-652.
Sukhatme BV. (1957). On certain two-sample nonparametric tests for variances. Annals of Mathematical Statistics 28: 188–194.
Wilcoxon F. (1945). Individual comparisons by ranking methods. Biometrics 1: 80-83.