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
7 results
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Now showing 1 - 7 of 7
Item Extension of the Wald statistic to models with dependent observations(Metrika, 2000) Morales González, Domingo; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen; Vadja, IgorA generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Levy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test.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 Choosing the best Rukhin goodness-of-fit statistics(Computational Statistics and Data Analysis, 2005) Marhuenda García, Yolanda; Morales González, Domingo; Pardo Llorente, Julio Ángel; Pardo Llorente, María del CarmenThe testing for goodness-of-fit in multinomial sampling contexts is usually based on the asymptotic distribution of Pearson-type chi-squared statistics. However, approximations are not justified for those cases where sample size and number of cells permit the use of adequate algorithms to calculate the exact distribution of test statistics in a reasonable time. In particular, Rukhin statistics, containing chi(2) and Neyman's modified chi(2) statistics, are considered for testing uniformity. Their exact distributions are calculated for different sample sizes and number of cells. Several exact power comparisons are carried out to analyse the behaviour of selected statistics. As a result of the numerical study some recommendations are given. Conclusions may be extended to testing the goodness of fit to a given absolutely continuous cumulative distribution function.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.Item A comparison of uniformity tests(Statistics: A Journal of Theoretical and Applied Statistics, 2005) Marhuenda García, Yolanda; Morales González, Domingo; Pardo Llorente, María del CarmenProblems of goodness-of-fit to a given distribution can usually be reduced to test uniformity. The uniform distribution appears due to natural random events or due to the application of methods for transforming samples from any other distribution to the samples with values uniformily distributed in the interval (0,1), Thus, one can solve the problem of testing if a sample comes from a given distribution by testing whether its transformed sample is distributed according to the uniform distribution. For this reason, the methods of testing for goodness-of-fit to a uniform distribution have been widely investigated. In this paper, a comparative power analysis of a selected set of statistics is performed in order to give suggestions on which one to use for testing uniformity against the families of alternatives proposed by Stephens [Stephens, M.A., 1974, EDF statistics for goodness of fit and some comparisons. Journal of the American Statistical Association, 69, 730-737.]. Definition and some relevant features of the considered test statistics are given in section 1. Implemented numerical processes to calculate percentage points of every considered statistic are described in section 2. Finally, a Monte Carlo simulation experiment has been carried out to fulfill the mentioned target of this paper.