Showing papers by "Hammou El Barmi published in 1999"
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TL;DR: In this paper, the estimation of a density f on the basis of random sample from a weighted distribution G with density g given by g(x) = w(xf(x)/Aµw, where w(u)>0 for all u and A ǫw = A¢Â« w (u)f(u )du
Abstract: In this paper we consider the estimation of a density f on the basis of random sample from a weighted distribution G with density g given by g(x) = w(x)f(x)/ Aµw, where w(u)>0 for all u and Aµw = A¢Â« w(u)f(u)du
22 citations
TL;DR: In this article, the authors investigated the joint behavior of the maximum likelihood estimators and lagrange multipliers corresponding to a null and alternative hypotheses defined by equality constraints, and used these results to test against a set of inequality constraints using the likelihood ratio approach.
Abstract: The first part of this article investigates the joint behaviour of the maximum likelihood estimators and lagrange multipliers corresponding to a null and alternative hypotheses defined by equality constraints. The results are then used to test against a set of inequality constraints using the likelihood ratio approach. This work is an extention of the results in Silvey (1959), El Barmi and Dykstra (1995) and Silvapulle (1994), and is closely connected with the work of Chernoff(1954); Robertson et al. (1988) and Self and Liang (1987). We show that the limiting distribution of the likelihood ratio test statistic under quite general conditions is of chi-bar square type and give an expression for the weighting values.
12 citations
TL;DR: In this article, the authors show that a dual problem always exits which is frequently more tractable and that a solution to the dual problem leads directly to a solution of the primal problem.
2 citations
TL;DR: In this article, the authors consider testing for and against decreasing in transposition in K×K×K contingency tables and show that when testing for exchangeability against this type of ordering, the asymptotic distribution of the likelihood ratio statistic is that of a convolution of several independent chi-bar square distributions.
1 citations