Goodness-of-fit testing with survival data

J. C. Escanciano, J. de Uña Álvarez

We develop a systematic, omnibus approach to goodness-of-fit testing for parametric distributional models under censoring and truncation. In many such designs, tests based on the nonparametric maximum likelihood estimator are hindered by nonexistence, computational instability, or convergence rates too slow to support reliable calibration under composite nulls. We avoid these difficulties by constructing a regular Neyman-orthogonal score process indexed by test functions, and aggregating it over a reproducing kernel Hilbert space ball. This yields a maximum-mean-discrepancy-type supremum statistic with a convenient quadratic-form representation. Critical values are obtained by bootstrapping. We establish asymptotic validity under the null and local alternatives and provide concrete constructions for left-truncated right-censored data, current status data, and random double truncation. Simulations and real data illustrations are included. Full paper at https://arxiv.org/abs/2602.08108

Keywords: Bootstrap, Censoring, Model assessment, Truncation

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