519.248 Cox model validity checking for several progressively censored samples

Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)

NONPARAMETRIC STATISTICS, KIEFER — GIHMAN TYPE CRITERION, KAPLAN — MEYER ESTIMATES, PROGRESSIVE CENSORING, COX MODEL


doi: 10.18698/2309-3684-2017-1-102117


The article proposes a nonparametric criterion of the Kiefer — Gihman type to test the Cox model validity for several progressively censored samples. As estimates of the reliability function for each sample we are using the Kaplan — Meyer ones. The paper proves that if the hypothesis is valid, the Kiefer — Gihman distribution can be used as an approximation of the asymptotic distribution of the criterionstatistics. Based on the particle random walk model over a multidimensional cells array, the paper has developed the method for calculating the exact statistics distributions. The article presents obtained probability values tables of the proposed statistics exact distributions for a wide range of samples possible values. Statistical modeling methods show Cox parameters estimating method consistency, based on the statistics minimization. We present the obtained estimates histograms for the developments exponential distribution to failure. The research results are used when analyzing the redundant technical systems of different multiplicity tests results operating in different operating conditions.
Analyzed systems find applications in all industries — from machine building to radio electronic.


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Timonin V., Tyannikova N. Cox model validity checking for several progressively censored samples. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 102-117



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