Person: Morales González, Domingo
Universidad Complutense de Madrid
Faculty / Institute
Estadística e Investigación Operativa
Now showing 1 - 10 of 22
PublicationExtension of the Wald statistic to models with dependent observations(Springer Heidelberg, 2000-12) 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. PublicationDivergence-based estimation and testing with misclassified data(Springer Verlag, 2005-07) Landaburu Jiménez, María Elena; Morales González, Domingo; Pardo Llorente, LeandroThe well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and phi-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum phi-divergence estimators are considered and some of their properties are established. The proposed phi-divergence test statistics are obtained by calculating phi-divergences between probability density functions and by replacing parameters by their minimum phi-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example PublicationInformational distances and related statistics in mixed continuous and categorical variables(Elsevier Science Bv, 1998-11-15) Morales González, Domingo; Pardo Llorente, Leandro; Zografos, KonstantinosA general class of dissimilarity measures among k greater than or equal to 2 distributions and their sample estimators are considered, for mixed continuous and categorical variables. The distributional properties are studied for the location model and the asymptotic distributions are investigated, in the general parametric case. The asymptotic distributions of the resulting statistics are used in various settings, to test statistical hypotheses. PublicationSome new statistics for testing hypotheses in parametric models(Academic Press, 1997-07) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper deals with simple and composite hypotheses in statistical models with i.i.d. observations and with arbitrary families dominated by a finite measures and parametrized by vector-valued variables. It introduces phi-divergence testing statistics as alternatives to the classical ones: the generalized likelihood ratio and the statistics of Wald and Rao. It is shown that, under the assumptions of standard type about hypotheses and model densities, the results about asymptotic distribution of the classical statistics established so far for the counting and Lebesgue dominating measures (discrete and continuous models) remain true also in the general case. Further, these results are extended to the phi-divergence statistics with smooth convex functions phi. The choice of phi-divergence statistics optimal from the point of view of power is discussed and illustrated by several examples. PublicationLikelihood divergence statistics for testing hypotheses about multiple population(Marcel Dekker Inc, 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. PublicationOn efficient estimation in continuous models based on finitely quantized observations(Taylor and Francis Inc., 2006) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorWe consider minimum phi-divergence estimators (theta) over cap (phi)(n) of parameters theta of arbitrary dominated models mu(theta) << lambda on the real line, based on finite quantizations of i.i.d. observations X-1,..., X-n from these models. The quantizations are represented by finite interval partitions P-n = (A(n1),...,A(nmn)) of the real line, where m(n) is allowed to increase to infinity for n --> infinity. The models with densities f(theta) = d mu(theta)/d lambda are assumed to be regular in the sense that they admit finite Fisher informations J(theta). In the first place we have in mind continuous models dominated by the Lebesgue measure lambda. Owing to the quantizations, (theta) over cap (phi)(n) are discrete-model estimators for which the desirable properties ( computation complexity, robustness, etc.) can be controlled by a suitable choice of functions phi. We formulate conditions under which these estimators are consistent and efficient in the original models mu(theta) in the sense that root n((theta) over cap (phi)(n)-theta) -->(L) N(0, J(theta)(-1)) as n --> infinity. PublicationLimit laws for disparities of spacings(Tailor and Francis, 2003-06) 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. PublicationAsymptotic laws for disparity statistics in product multinomial models(Academic Press, 2003-05) Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper presents asymptotic distributions of phi-disparity goodness-of-fit statistics in product multinomial models, under hypotheses and alternatives assuming sparse and nonsparse cell frequencies. The phi-disparity statistics include the power divergences of Read and Cressie (Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York, 1988), the phi-divergences of Ciszar (Studia Sci. Math. Flungar. 2 (1967) 299) and the robust goodness of fit statistics of Lindsay (Ann. Statist. 22 (1994) 1081). PublicationApproximations to powers of phi-disparity goodness-of-fit tests(Marcel Dekker Inc., 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper studies a class of tests based on disparities between the real-valued data and theoretical models resulting either from fixed partitions of the observation space, or from the partitions by the sample quantiles of fixed orders. In both cases there are considered the goodness-of-fit tests of simple and composite hypotheses. All tests are shown to be consistent, and their power is evaluated at the nonlocal as well as local alternatives. PublicationStatistical inference for finite Markov chains based on divergences(Elsevier Science Bv., 1999-06-01) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Zografos, KonstantinosWe consider statistical data forming sequences of states of stationary finite irreducible Markov chains, and draw statistical inference about the transition matrix. The inference consists in estimation of parameters of transition probabilities and testing simple and composite hypotheses about them. The inference is based on statistics which are suitable weighted sums of normed phi-divergences of theoretical row distributions, evaluated at suitable points, and observed empirical row distributions. The asymptotic distribution of minimum phi-divergence estimators is obtained, as well as critical values of asymptotically alpha-level tests.