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Article

Keywords:
hazard rate; counting process; Cox model; nonparametric regression; local likelihood; time-to-failure
Summary:
The contribution deals with an application of the nonparametric version of Cox regression model to the analysis and modeling of the failure rate of technical devices. The objective is to recall the method of statistical analysis of such a model, to adapt it to the real–case study, and in such a way to demonstrate the flexibility of the Cox model. The goodness-of-fit of the model is tested, too, with the aid of the graphical test procedure based on generalized residuals.
References:
[1] Andersen P. K., Borgan O., Gill R. D., Keiding N.: Statistical Models Based on Counting Processes. Springer, New York 1993 MR 1198884 | Zbl 0824.60003
[2] Arjas E.: A graphical method for assesing goodnes of fit in Cox’s proportional hazard model. J. Amer. Statist. Assoc. 83 (1988), 204–212 DOI 10.1080/01621459.1988.10478588
[3] Arjas E., Liu L.: Assessing the losses caused by an industrial intervention – a hiearchical Bayesian approach. J. Roy. Statist. Soc. Ser. C 44 (1995), 357–368
[4] Fan J., Gijbels I.: Local Polynomial Modelling and Its Applications. Chapman and Hall, London 1996 MR 1383587 | Zbl 0873.62037
[5] Gentleman R., Crowley J.: Local full likelihood estimation for the proportional hazard model. Biometrics 47 (1991), 1283–1296 DOI 10.2307/2532386 | MR 1157661
[6] Hastie T., Tibshirani R.: Generalized Additive Models. Chapman and Hall, London 1990 MR 1082147 | Zbl 0747.62061
[7] Kalbfleisch J. D., Struthers C. A.: An analysis of the Reynolds Metals Company data. In: Case Studies in Data Analysis, Canad. J. Statist. 10 (1982), 237–259 DOI 10.2307/3556191
[8] Kooperberg C., Stone C. J., Truong Y. K.: The $L_2$ rate of convergence for hazard regression. Scand. J. Statist. 22 (1995), 143–157 MR 1339748
[9] Marzec L., Marzec P.: Generalized martingale-residual processes for goodness-of-fit inference in Cox’s type regression model. Ann. Statist. 25 (1997), 683–714 DOI 10.1214/aos/1031833669 | MR 1439319
[10] O’Sullivan F.: Nonparametric estimation in the Cox model. Ann. Statist. 21 (1993), 124–145 DOI 10.1214/aos/1176349018 | MR 1212169 | Zbl 0782.62046
[11] Stone C. J.: The use of polynomial splines and their tensor products in multivariate function estimation; with discussion. Ann. Statist. 22 (1994), 118–184 DOI 10.1214/aos/1176325361 | MR 1272079 | Zbl 0827.62038
[12] Thomas D. C.: Case analysis using Cox’s model. In: Case Studies in Data Analysis. Canad. J. Statist. 10 (1982), 237–259 DOI 10.2307/3556191
[13] Volf P.: A large sample study of nonparametric proportion hazard regression model. Kybernetika 29 (1993), 404–415 MR 1079678
[14] Volf P.: Analysis of generalized residuals in hazard regression models. Kybernetika 32 (1996), 501–510 MR 1420139 | Zbl 0882.62077
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