Inference and Thick Tails: Some Surprising Results
AbstractThis paper analyses the distribution of the classical t-ratio statistic from distributions with no finite moments and shows how classical testing is affected. Some surprising results are obtained in terms of bimodality vs. the usual unimodality of the standard studentized t-distribution prevailing in classical conditions. The paper develops a new distribution termed the “double Pareto,” which allows the thickness of the tails and the existence of moments to be determined parametrically. We also consider infinite-moments distributions truncated on a compact support to investigate the relative importance of tail thickness in case of finite moments. We find that the bimodality persists even in such cases. Simulation results are used to highlight the dangers of relying on naive testing in the face of thick-tailed distributions. Special cases analyzed include one- and two-sample statistical inference problems, as well as linear regression econometric problems.
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Bibliographic InfoPaper provided by Universitá degli Studi di Milano in its series UNIMI - Research Papers in Economics, Business, and Statistics with number unimi-1054.
Date of creation: 03 May 2007
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thick-tailed distributions; studentized t-distribution; Pareto distribution; bimodality; truncated distribution;
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