Tailor-made tests for goodness of fit to semiparametric hypotheses

By Peter J. Bickel, Yaacov Ritov, Thomas M. Stoker. 2006

77 citations recorded by the source corpus.

1. Introduction. The practice of statistical testing plays several roles inempirical research. These roles range from the careful assessment of theevidence against speciﬁc scientiﬁc hypotheses to the judgment of whetheran estimated model displays decent goodness of ﬁt to the empirical data.The paradigmatic situation we consider is one where the investigator viewssome departures from the hypothesized model as being of primary impor-tance, with others of interest if suﬃciently gross, but otherwise secondary.For instance, low-frequency departures from a signal hypothesized to beconstant might be considered of interest, even if of low amplitude; whilehigh-frequency departures are less so, unless they are of high amplitude.The optimal testing of a simple hypothesis against a simple alternativeis the cornerstone of modern statistical theory. However, there is no clearnotion of optimality for more complicated situations. The H´ajek–Le Camasymptotic theory proved that there exist strong concepts of asymptotic ef-ﬁciency in parametric estimation. These ideas have been extended to semi-parametric models—see [3, 14, 22]. However, there is no compelling sense ofan asymptotically optimum test, in either the parametric or the semipara-metric asymptotic theories, save for some simple one-parameter hypotheses.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a677f4541107def6832bc8ae0a78d2c27565a907

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Citations in the corpus

: "Statistical Modeling: The Two Cultures" (Statistical Science, 2001, 16(3), 199-231) (unknown): “Bickel et al. (2006) established that goodness of ﬁt tests have extremely low power unless the direction of the alternative is precisely speciﬁed.”
ABC–CDE: Toward Approximate Bayesian Computation With Complex High-Dimensional Data and Limited Simulations (2018, background): “Some density estimates which are not close to the true density can pass all tests (Breiman, 2001; Bickel et al., 2006), and the situation is even worse in conditional density estimation.”