Goodness-of-fit tests via ϕ-measures of divergence for censored data

REFERENCES

• S. Kullback and R. Leibler, On information and sufficiency, Ann. Math. Statist. 22 (1951), pp. 79–86. doi: 10.1214/aoms/1177729694
   Google Scholar
• I. Csiszar, Eine Informationstheoretische Ungleichung und ihre Anwendung auf den Bewis der Ergodizitat on Markhoffschen Ketten, Publication of the Mathematical Institute of the Hungarian Academy of Science Vol. 8, 1963, pp. 84–108.
   Google Scholar
• S.M. Ali, and S.D. Silvey, A general class of coefficients of divergence of one distribution from another, J. R. Statist. Soc. B 28 (1966), pp. 131–142.
   Google Scholar
• N. Cressie and T.R.C. Read, Multinomial goodness-of-fit tests, J.R. Statist. Soc 5 (1984), pp. 440–454.
   Google Scholar
• A. Basu, I.R. Harris, N.L. Hjort, and M.C. Jones, Robust and efficient estimation by minimising a density power divergence, Biometrika 85 (1998), pp. 549–559. doi: 10.1093/biomet/85.3.549
   Web of Science ®Google Scholar
• K. Mattheou, S. Lee, and A. Karagrigoriou, A model selection criterion based on the BHHJ measure of divergence, J. Statist. Plann. Inference 139 (2009), pp. 128–135. doi: 10.1016/j.jspi.2008.04.022
   Web of Science ®Google Scholar
• L. Pardo, Statistical Inference Based on Divergence Measures, Chapman & Hall/CRC, Boca Raton, FL, 2006.
   Google Scholar
• A. Toma, Minimum Hellinger distance estimators for multivariate distributions from the Johnson system, J. Statist. Plann. Inference 138 (2008), pp. 803–816.
   Google Scholar
• A. Toma, Optimal robust M-estimators using divergences, Statist. Probab. Lett. 79 (2009), pp. 1–5. doi: 10.1016/j.spl.2008.04.011
   Web of Science ®Google Scholar
• C. Huber-Carol, N. Balakrishnan, M.S. Nikulin, and M. Mesbah, Goodness-of-Fit Tests and Model Validity, Birkhäuser, Boston, MA, 2002.
   Google Scholar
• J. Zhang, Powerful goddness-of-fit tests based on likelihood ratio, J.R. Stat. Soc. Ser. B 64 (2002), pp. 281–294. doi: 10.1111/1467-9868.00337
   Google Scholar
• J.E. Cavanaugh, Criteria for linear model selection based on Kullback's symmetric divergence, Aust. N. Z. J. Stat. 46 (2004), pp. 257–274. doi: 10.1111/j.1467-842X.2004.00328.x
   Web of Science ®Google Scholar
• J. Shang, Selection criteria based on Monte Carlo simulation and cross validation in mixed models, Far East J. Theor. Stat. 25 (2008), pp. 51–72.
   Google Scholar
• M.H. Gail and J.H. Ware, Comparing observed life table data with a known survival curve in the presence of random censorship, Biometrics 35 (1979), pp. 385–391. doi: 10.2307/2530341
   Web of Science ®Google Scholar
• M.G. Akritas, Pearson-type goodness-of-fit tests: The univariate case, J. Amer. Statist. Assoc. 83 (1988), pp. 222–230. doi: 10.1080/01621459.1988.10478590
   Web of Science ®Google Scholar
• H.S. Chen, K. Lai, and Z. Ying, Goodness of fit tests and minimum power divergence estimators for survival data, Statist. Sinica 14 (2004), pp. 231–248.
   Web of Science ®Google Scholar
• A.M. Kagan, On the theory of Fisher's amount of information, Sov. Math. Dokl. 4 (1963), pp. 991–993.
   Google Scholar
• K. Matusita, On the notion of affinity of several distributions and some of its applications, Ann. Inst. Statist. Math. 19 (1967), pp. 181–192. doi: 10.1007/BF02911675
   Web of Science ®Google Scholar
• K. Mattheou and A. Karagrigoriou, A new family of divergence measures for tests of fit, Aust. N. Z. J. Stat. 52 (2010), pp. 187–200. doi: 10.1111/j.1467-842X.2010.00574.x
   Web of Science ®Google Scholar
• R.J. Serfling, Approximation Theorems of Mathematical Statistics, Wiley, New York, 1980.
   Google Scholar
• D. Hunter, Lecture Notes in Asymptotic Tools, Penn-State University, 2002. Available at http://www.stat.psu.edu/dhunter/asymp/fall2002/lectures/ln11.pdf
   Google Scholar
• R.S. Chhikara and J.L. Folks, The inverse Gaussian distribution as a lifetime model, Technometrics 19 (1977), pp. 461–468.
   Google Scholar
• A. Tsanousa, Statistical inference via ϕ-measures of divergence, Master thesis, National Technical University of Athens (in Greek), 2010.
   Google Scholar
• T.W. Anderson and D.A. Darling, A test of goodness of fit, J. Amer. Statist. Assoc. 49 (1954), pp. 765–769. doi: 10.1080/01621459.1954.10501232
   Web of Science ®Google Scholar
• H. Cramér, On the composition of elementary errors, Skand. Aktuarietids 11 (1928), pp. 13–74, 141–180.
   Google Scholar
• F.J. O'Reilly and R. Rueda, Goodness of fit for the inverse Gaussian distribution, Canad. J. Statist. 20 (1992), pp. 387–397. doi: 10.2307/3315609
   Web of Science ®Google Scholar
• R. Edgeman, R. Scott, and R. Pavur, A modified Kolmogorov-Smirnov test for the inverse Gaussian density with unknown parameters, Comm. Statist. Simulation Comput. 17 (1988), pp. 1203–1212. doi: 10.1080/03610918808812721
   Web of Science ®Google Scholar
• H. Gunes, D.C. Dietz, P.F. Auclair, and A.H. Moore, Modified goodness-of-fit tests for the inverse Gaussian distribution, Comput. Stat. Data Anal. 24 (1997), pp. 63–77. doi: 10.1016/S0167-9473(96)00056-4
   Web of Science ®Google Scholar
• I.A. Koutrouvelis, G. Canavos, and A. Kallioras, Cumulant plots for assessing the Gamma distribution, Commun. Stat. Theory Methods 39 (2010), pp. 626–641. doi: 10.1080/03610920902774244
   Web of Science ®Google Scholar
• V. Susarla and J. van Ryzin, Empirical Bayes estimation survival distribution function from right censored data, Anal. Statist. 6 (1978), pp. 740–755. doi: 10.1214/aos/1176344249
   Web of Science ®Google Scholar
• B. Efron, Logistic regression, survival analysis and the Kaplan–Meier curve, J. Amer. Statist. Assoc. 83 (1988), pp. 414–425. doi: 10.1080/01621459.1988.10478612
   Web of Science ®Google Scholar
• M.S. Nikulin and F. Haghighi, A chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data, J. Math. Sci. 133 (2004), pp. 1333–1341. doi: 10.1007/s10958-006-0043-8
   Google Scholar
• N. Saaidia, A chi-squared test for the family of inverse Gaussian distributions for censored data, Proceedings of International Workshop on Applied Methods of Statistical Analysis. Simulations and Statistical Inference, B. Lemeshko, M. Nikulin, and N. Balakrishnan, eds, Publishing House of NSTU, Novosibirsk, 2011, pp. 167–175.
   Google Scholar