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April 1997 Generalized martingale-residual processes for goodness-of-fit inference in Cox's type regression models
Leszek Marzec, Paweł Marzec
Ann. Statist. 25(2): 683-714 (April 1997). DOI: 10.1214/aos/1031833669


In the paper a general class of stochastic processes based on the sums of weighted martingale-transform residuals for goodness-of-fit inference in general Cox's type regression models is studied. Their form makes the inference robust to covariate outliers. A weak convergence result for such processes is obtained giving the possibility of establishing the randomness of their graphs together with the construction of the formal $\chi^2$-type goodness-of-fit tests. By using the Khmaladze innovation approach, a modified version of the initial class of processes is also defined. Weak convergence results for the processes are derived. This leads to the main application which concerns the formal construction of the Kolmogorov-Smirnov and Cramér-von Mises-type goodness-of-fit tests. This is done within the general situation considered.


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Leszek Marzec. Paweł Marzec. "Generalized martingale-residual processes for goodness-of-fit inference in Cox's type regression models." Ann. Statist. 25 (2) 683 - 714, April 1997.


Published: April 1997
First available in Project Euclid: 12 September 2002

zbMATH: 0909.62049
MathSciNet: MR1439319
Digital Object Identifier: 10.1214/aos/1031833669

Primary: 62F12
Secondary: 62G10 , 62G20

Keywords: Censoring , counting process , Cox-regression , Goodness-of-fit , innovation process , martingale , residual , robust inference , Survival analysis , weak convergence

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 2 • April 1997
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