Person: Morales González, Domingo
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First Name
Domingo
Last Name
Morales González
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Estadística e Investigación Operativa
Identifiers
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Item Rényi statistics for testing composite hypotheses in general exponential models.(Statistics, 2004) Morales González, Domingo; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen; Vadja, IgorWe introduce a family of Renyi statistics of orders r is an element of R for testing composite hypotheses in general exponential models, as alternatives to the previously considered generalized likelihood ratio (GLR) statistic and generalized Wald statistic. If appropriately normalized exponential models converge in a specific sense when the sample size (observation window) tends to infinity, and if the hypothesis is regular, then these statistics are shown to be chi(2)-distributed under the hypothesis. The corresponding Renyi tests are shown to be consistent. The exact sizes and powers of asymptotically alpha-size Renyi, GLR and generalized Wald tests are evaluated for a concrete hypothesis about a bivariate Levy process and moderate observation windows. In this concrete situation the exact sizes of the Renyi test of the order r = 2 practically coincide with those of the GLR and generalized Wald tests but the exact powers of the Renyi test are on average somewhat better.Item Limit laws for disparities of spacings(Journal of Nonparametric Statistics, 2003) Morales González, Domingo; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen; Vadja, IgorDisparities 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 Likelihood divergence statistics for testing hypotheses about multiple population(Communications in Statistics - Simulation and Computation, 2001) Morales González, Domingo; Pardo Llorente, Leandro; Pardo Llorente, María del CarmenThe problem of introducing divergence-based statistics to test composite hypotheses related to s populations is still open when sample sizes are not equal. On the basis of likelihood divergence statistics, a statistical procedure is introduced in this paper and its large sample behaviour is studied. By using Renyi divergence, the proposed statistical procedure is applied to the problem of testing for the homogeneity of several variances. Members of the family of likelihood Renyi divergence statistics are compared for power and checked for fidelity to type I error rates with some classical test statistics. Results of the Monte Carlo simulation study are discussed and presented in tables.Item Rukhin's uniformity test based on sample quantiles(Journal of Statistical Computation and Simulation, 2005) Marhuenda García, Yolanda; Morales González, Domingo; Pardo Llorente, Julio Ángel; Pardo Llorente, María del CarmenThe problem of testing if a given probability distribution fits to a set of independent and identically distributed observations is usually treated by categorizing the data range. Discretization can be done by means of relative frequencies or by using sample quantiles. In this article, quantile-based test statistics are proposed to test the hypothesis of uniformity in the interval (0, 1). Exact critical values of the family of Rukhin's statistics are estimated. A Monte Carlo simulation experiment is carried out to calculate powers of these tests in different alternatives. Results obtained from each kind of categorization are compared to give several recommendations about the use of Rukhin's statistics and type of categorization.