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Limit laws for disparities of spacings

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Morales González, Domingo and Pardo Llorente, Leandro and Pardo Llorente, María del Carmen and Vadja, Igor (2003) Limit laws for disparities of spacings. Journal of Nonparametric Statistics, 15 (3). pp. 325-342. ISSN 1048-5252

Official URL: http://www.tandfonline.com/doi/abs/10.1080/1048525031000120206


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Abstract

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.


Item Type:Article
Uncontrolled Keywords:spacings; disparities of spacings under a hypothesis; limit laws for disparities of m-spacings; goodness-of-fit tests based on disparities of spacings; high-order spacings; asymptotic distributions; sample spacings; statistics; theorems; tests; divergence; goodness; sums
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:17810
Deposited On:21 Jan 2013 10:21
Last Modified:21 Jan 2013 10:21

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