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
5 results
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Item Asymptotic distributions of phi-divergences of hypothetical and observed frequencies on refined partitions(Statistica Neerlandica, 1988) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorFor a wide class of goodness-of-fit statistics based on phi-divergences between hypothetical cell probabilities and observed relative frequencies, the asymptotic normality is established under the assumption n/m(n) --> gamma is an element of (0, infinity), where n denotes sample size and m(n) the number of cells. Related problems of asymptotic distributions of phi-divergence errors, and of phi-divergence deviations of histogram estimators from their expected values, are considered too.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 Asymptotic laws for disparity statistics in product multinomial models(Journal of multivariate analysis, 2003) 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).Item Some new statistics for testing hypotheses in parametric models(Journal of multivariate analysis, 1997) 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.Item Minimum divergence estimators based on grouped data(Annals of the Institute of Statistical Mathematics, 2001) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorThe paper considers statistical models with real-valued observations i.i.d. by F(x, theta (0)) from a family of distribution functions (F(x, theta); theta is an element of Theta), Theta subset of R-s, s greater than or equal to 1. For random quantizations defined by sample quantiles (F-n(-1)(lambda (1)),..., F-n(-1)(lambda (m-1))) of arbitrary fixed orders 0 < (1) < ... < lambda (m-1) < 1, there are studied estimators (phi ,n) of theta (0) which minimize phi -divergences of the theoretical and empirical probabilities. Under an appropriate regularity, all these estimators are shown to be as efficient (first order, in the sense of Rao) as the MLE in the model quantified nonrandomly by (F-1(lambda (1), theta (0)),..., F-1(lambda (m-1), theta (0))). Moreover, the Fisher information matrix I-m(theta (0), lambda) of the latter model with the equidistant orders lambda = (lambda (j) = j/m : 1 less than or equal to j less than or equal to m-1) arbitrarily closely approximates the Fisher information F(theta (0)) of the original model when m is appropriately large. Thus the random binning by a large number of quantiles of equidistant orders leads to appropriate estimates of the above considered type.