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Weighted Integral Test Statistics and Components of Smooth Tests of Fit

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This paper considers families of statistics for testing the goodness-of-fit of various parametric models such as the normal, exponential or Poisson. Each family consists of weighted integrals over the squared modulus of some measure of deviation from the parametric model, expressed by means of an empirical transform of the data. Letting the rate of decay of the weight function tend to infinity, each test statistic, after a suitable rescaling, approaches a limit that is closely connected to the first non-zero component of Neyman's smooth test for the parametric model.
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Keywords: Abelian theorem; empirical Laplace transform; empirical characteristic function; empirical probability generating function; goodness-of-fit test; smooth test of fit.

Document Type: Research Article

Affiliations: 1: Universitäat Hannover, Institut für Mathematische Stochastik, Welfengarten 1, 30167 Hannover, Germany. 2: Universität Karlsruhe, Institut für Mathematische Stochastik, Englerstr. 2, 76128 Karlsruhe, Germany. Email: [email protected]

Publication date: June 1, 2000

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