no. 3-4
Statistics/Probability Theory
Chi-squared tests for general composite hypotheses from censored samples
[Tests chi carré pour des hypothèses composites généralisées des données censurées]

Présenté par : Paul Deheuvels

Bagdonavičius, Vilijandas1 ; Nikulin, Mikhail2
1 University of Vilnius, 24, Naugarduko, 03225 Vilnius, Lithuania
2 Université Victor-Segalen, 33000 Bordeaux, France
Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 219-223.

On propose des tests d'ajustement du type chi carré pour des modèles paramétriques y compris les modèles de la vie accélerée, de Cox, de risques proportionnels généralisés, de transformations et d'autres. Le choix de limites des intervales de groupement comme fonctions des données est considéré.

We give chi-squared goodness-of-fit tests for parametric models including various regression models such as accelerated failure time, proportional hazards, generalized proportional hazards, frailty models, transformation models, models with cross-effects of survival functions. Choice of random grouping intervals as data functions is considered.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.007
Bagdonavičius, Vilijandas 1 ; Nikulin, Mikhail 2

1 University of Vilnius, 24, Naugarduko, 03225 Vilnius, Lithuania
2 Université Victor-Segalen, 33000 Bordeaux, France 
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Bagdonavičius, Vilijandas; Nikulin, Mikhail. Chi-squared tests for general composite hypotheses from censored samples. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 219-223. doi : 10.1016/j.crma.2011.01.007. http://www.numdam.org/articles/10.1016/j.crma.2011.01.007/

[1] Aalen, O. Nonparametric inference for the family of counting processes, Ann. Statist., Volume 6 (1978), pp. 701-726

[2] Akritas, M.G. Pearson-type goodness-of-fit tests: the univariate case, J. Amer. Statist. Assoc., Volume 83 (1988), pp. 222-230

[3] Akritas, M.G.; Torbeyns, A.F. Pearson-type goodness-of-fit tests for regression, Canad. J. Statist., Volume 25 (1997), pp. 359-374

[4] Andersen, P.K.; Borgan, O.; Gill, R.D.; Keiding, N. Statistical Models Based on Counting Processes, Springer-Verlag, New York, 1993

[5] Bagdonavičius, V. Testing the hyphothesis of the additive accumulation of damages, Probab. Theory Appl., Volume 23 (1978), pp. 403-408

[6] Bagdonavičius, V.; Nikulin, M. Accelerated Life Models, Chapman and Hall/CRC, Boca Raton, 2002

[7] Billingsley, P. Convergence of Probability Measures, Wiley, New York, 1968

[8] Gray, R.J.; Pierce, D.A. Goodness of fit tests for censored survival data, Ann. Statist., Volume 13 (1985), pp. 552-563

[9] Greenwood, P.; Nikulin, M.S. A Guide to Chi-squared Testing, Wiley, New York, 1996

[10] Habib, M.G.; Thomas, D.R. Chi-squared goodness-of-fit tests for randomly censored data, Ann. Statist., Volume 14 (1986), pp. 759-765

[11] Hjort, N.L. Goodness of fit tests in models for life history data based on cumulative hazard rates, Ann. Statist., Volume 18 (1990), pp. 1221-1258

[12] Hollander, M.; Peña, E. Chi-square goodness-of-fit test for randomly censored data, JASA, Volume 417 (1992), pp. 458-463

[13] Koul, H. Tests of goodness-of-fit in linear regression, Colloq. Math. Soc. János Bolyai, Volume 45 (1984), pp. 279-315

[14] LeCam, L.; Mahan, C.; Singh, A. An extension of a theorem of H. Chernoff and E.L. Lehmann, Recent Advances in Statistics, Academic Press, Orlando, 1983, pp. 303-332

[15] Loynes, R.M. The empirical distribution function of residuals from generalized regression, Ann. Statist., Volume 8 (1980), pp. 285-298

[16] Mukantseva, L.A. Testing normality in one-dimensional and multi-dimensional linear regression, Theory Probab. Appl., Volume 22 (1977), pp. 591-602

[17] Nikulin, M.S. Chi-square test for continuous distribution with shift and scale parameters, Theory Probab. Appl., Volume 19 (1973), pp. 559-568

[18] Pierce, D.; Kopecky, K. Testing goodness of fit for the distribution of errors in regression models, Biometrika, Volume 66 (1979)

[19] Rao, K.C.; Robson, D.S. A chi-square statistic for goodness-of-fit tests within the exponential family, Comm. Statist., Volume 3 (1974), pp. 1139-1153

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