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In the univariate continuous goodness-of-fit problem, the probability integral transformation (PIT) is used to transform the sample observations into the unit interval when the distribution to be tested is completely specified (the simple case); thus reducing the problem to that of testing uniformity of the transforms. The asymptotic theory for the induced empirical process in (0,1) is well known and so, that of functionals of it, including the so called EDF tests that are based on the Empirical Distribution Function ( see Tests of fit based on the empirical distribution function).

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Exact Goodness-of-fit Tests Based on Sufficiency

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  • 发表日期：

    2025年

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  • Federico J. O’Reilly Togno,
  • Leticia Gracia-Medrano

摘要

In the univariate continuous goodness-of-fit problem, the probability integral transformation (PIT) is used to transform the sample observations into the unit interval when the distribution to be tested is completely specified (the simple case); thus reducing the problem to that of testing uniformity of the transforms. The asymptotic theory for the induced empirical process in (0,1) is well known and so, that of functionals of it, including the so called EDF tests that are based on the Empirical Distribution Function ( see Tests of fit based on the empirical distribution function).