Parametric bootstrap tests for continuous and discrete distributions |
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Authors: | Gábor Sz?cs |
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Institution: | (1) Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, 6720 Szeged, Hungary |
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Abstract: | Statistical procedures based on the estimated empirical process are well known for testing goodness of fit to parametric distribution
families. These methods usually are not distribution free, so that the asymptotic critical values of test statistics depend
on unknown parameters. This difficulty may be overcome by the utilization of parametric bootstrap procedures. The aim of this
paper is to prove a weak approximation theorem for the bootstrapped estimated empirical process under very general conditions,
which allow both the most important continuous and discrete distribution families, along with most parameter estimation methods. The emphasis is on families of discrete distributions,
and simulation results for families of negative binomial distributions are also presented. |
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Keywords: | Bootstrap Parametric estimation Empirical process Approximation Convergence in distribution |
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