RT Journal Article
T1 Limit laws for disparities of spacings
A1 Morales González, Domingo
A1 Pardo Llorente, Leandro
A1 Pardo Llorente, María del Carmen
A1 Vadja, Igor
AB 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.
PB Tailor and Francis
SN 1048-5252
YR 2003
FD 2003-06
LK https://hdl.handle.net/20.500.14352/50309
UL https://hdl.handle.net/20.500.14352/50309
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RD 8 may 2024