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
6 results
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Now showing 1 - 6 of 6
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 Informational distances and related statistics in mixed continuous and categorical variables(Journal of Statistical Planning and Inference, 1998) 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.Item Statistical inference for finite Markov chains based on divergences(Statistics and probability letters, 1999) 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.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 φ-divergences and nested models.(Applied Mathematics Letters, 1997) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, LeandroWe consider a wide class of statistics, namely phi-divergences. We obtain asymptotic distributions of these statistics in nested models. Our result generalizes previous results in this field.Item Two approaches to grouping of data and related disparity statistics(Communications in statistics. Theory and methods, 1988) Menéndez Calleja, María Luisa; Morales González, Domingo; Pardo Llorente, Leandro; Vadja, IgorCsiszar's phi-divergences of discrete distributions are extended to a more general class of disparity measures by restricting the convexity of functions phi(t), t > 0, to the local convexity at t = 1 and monotonicity on intervals (0, 1) and (1, infinity). Goodness-of-fit estimation and testing procedures based on the phi-disparity statistics are introduced. Robustness of the estimation procedure is discussed and the asymptotic distributions for the testing procedure are established in statistical models with data grouped according to their values or orders.