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Title: The likelihood ratio test of independence for random size samples Authors:  Carlos Coelho - NOVA University of Lisbon (Portugal) [presenting]
Filipe Marques - Centro de Matemática e Aplicações (CMA) and Departamento de Matemática, FCT, NOVA University of Lisbon (Portugal)
Abstract: The focus is on the distribution of the likelihood ratio test statistic used to test the independence of two sets of variables when samples have random sizes, originated from different underlying distributions, namely Poisson, Binomial and Negative Binomial. Situations are identified when the distribution of the statistic has closed finite form representations, while for the other situations sharp approximations are developed, being shown how sharp upper bounds on the approximation error may be obtained. Using a real data set, the test is performed assuming, for the derivation of the distribution of the likelihood ratio statistic, a random sample size and the results are compared with the ones obtained using the traditional approach.