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Goodness of Fit Tests for Multivariate Counting Process Models with Applications
Author(s) -
Sun Yanqing,
Tiwari Ram C.,
Zalkikar Jyoti N.
Publication year - 2001
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00234
Subject(s) - mathematics , martingale (probability theory) , counting process , goodness of fit , multiplicative function , multivariate statistics , residual , statistics , consistency (knowledge bases) , parametric statistics , algorithm , mathematical analysis , discrete mathematics
In this paper, we develop some distribution‐free tests for checking the adequacy of the parametric forms of the intensity processes of a multivariate counting process model. The proposed tests, based in Khmaladze's transformations, are derived from the transforms of weighted aggregated martingale residual processes. The transformed processes converge weakly to independent Gaussian martingales under the assumed model. The distribution‐free tests, such as Kolmogorov–Smirnov and Cramer–von Mises type tests, are appropriately defined to account for deviations in each of the transformed aggregated martingale residual processes. Consistency of the tests are discussed. The tests are applicable to multiplicative intensity models such as a competing risks model as well as to non‐multiplicative intensity models such as a constant relative or excess mortality model. A small simulation study is conducted and an illustration to a real data example is provided.