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Analysis of generalized residuals in hazard regression models. (English) Zbl 0882.62077
Summary: We consider a counting process and a model of its intensity. We introduce the generalized residuals measuring the deviation of observed times to counts from the expected times given by the model. These residuals are then used for assessing the goodness-of-fit of hazard regression models. The method is inspired by E. Arjas’ [J. Am. Stat. Assoc. 83, 204-212 (1988)] graphical procedure (dealing with Cox’s model) and generalized to a quite general hazard regression case. The large sample properties of the test statistics are derived, they are then specified for the case of Aalen’s regression model. The diagnostic ability of the method is illustrated by an example with simulated data.

62M07 Non-Markovian processes: hypothesis testing
62-09 Graphical methods in statistics (MSC2010)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
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