%0 Journal Article
%A Morales González, Domingo
%A Pardo Llorente, Leandro
%A Pardo Llorente, María del Carmen
%A Vadja, Igor
%T Limit laws for disparities of spacings
%D 2003
%@ 1048-5252
%U https://hdl.handle.net/20.500.14352/50309
%X Disparities of spacings mean the phi-disparities D-phi((q) over bar (n), p(n)) of discrete hypothetical and empirical distributions g and p(n) defined by m-spacings on i.i.d. samples of size n where phi: (0, infinity) \--> HR is twice continuously differentiable in a neighborhood of 1 and strictly convex at 1. It is shown that a slight modification of the disparity statistics introduced for testing the goodness-of-fit in 1986 by Hall are the phi-disparity statistics D-n(phi) = nD(phi) ((q) over bar (n), p(n)). These modified statistics can be ordered for 1 less than or equal to m less than or equal to n as to their sensitivity to alternatives. The limit laws governing for n --> infinity the distributions of the statistics under local alternatives are shown to be unchanged by the modification, which allows to construct the asymptotically a-level goodness-of-fit tests based on D-n(phi). In spite of that the limit laws depend only on the local properties of phi in a neighborhood of 1, we show by a simulation that for small and medium sample sizes n the true test sizes and powers significantly depend on phi and also on the alternatives, so that an adaptation of phi to concrete situations can improve performance of the phi-disparity test. Relations of D-n(phi) to some other m-spacing statistics known from the literature are discussed as well.
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