Abstract: Goodness of fit procedures are essential tools for assessing model adequacy. In this work, we present a general theory and approach to goodness of fit techniques based on U-processes for the accelerated failure time (AFT) model. Many of the examples focus on U-statistics of order 2. While many authors have proposed goodness of fit tests for U-statistics of order one, less has been developed for higher order U-statistics. We propose goodness of fit tests for U-statistics of order 2 by using theoretical results from Nolan and Pollard (1987) and Nolan and Pollard (1988). We advance a resampling approach that is a generalization of the one proposed in Lin, Robins and Wei (1996). Simulation studies are used to illustrate the proposed methods.

Key words and phrases: U-statistics, Gaussian process, perturbation method, survival analysis.