2026-06-28T20:11:02Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/503092023-08-26T13:11:18Zcom_20.500.14352_14col_20.500.14352_15

Limit laws for disparities of spacings Morales González, Domingo Pardo Llorente, Leandro Pardo Llorente, María del Carmen Vadja, Igor 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. 2023-06-20T09:45:26Z 2023-06-20T09:45:26Z 2023-06-20T09:45:26Z 2003-06 journal article https://hdl.handle.net/20.500.14352/50309 1048-5252 10.1080/1048525031000120206 metadata only access Tailor and Francis