Person: Pardo Llorente, Leandro
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First Name
Leandro
Last Name
Pardo Llorente
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
Identifiers
33 results
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Now showing 1 - 10 of 33
Item Rao's statistic for the analysis of uniform association in cross-classifications(Communications in statistics. Theory and methods, 2001) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, LeandroIn this paper we introduce a new measure for the analysis of association in cross-classifications having ordered categories. Association is measured in terms of the odd-ratios in 2 x 2 subtables formed from adjacent rows and adjacent columns. We focus our attention in the uniform association model. Our measure is based in the family of divergences introduced by Burbea and Rao [1]. Some well-known sets of data are reanalyzed and a simulation study is presented to analyze the behavior of the new families of test statistics introduced in this paper.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 Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model(Statistical Papers, 2009) Menéndez Calleja, María Luisa; Pardo Llorente, Leandro; Pardo Llorente, María del CarmenThe problem of estimation of the parameters in a logistic regression model is considered under multicollinearity situation when it is suspected that the parameter of the logistic regression model may be restricted to a subspace. We study the properties of the preliminary test based on the minimum phi-divergence estimator as well as in the phi-divergence test statistic. The minimum phi-divergence estimator is a natural extension of the maximum likelihood estimator and the phi-divergence test statistics is a family of the test statistics for testing the hypothesis that the regression coefficients may be restricted to a subspace.Item Selection of the best population: an information theoretic approach(Metrika, 2003) Menéndez Calleja, María Luisa; Pardo Llorente, Leandro; Tsairidis, Ch.; Zografos, KonstantinosThis paper is devoted to the statistical problem of ranking and selection populations by using the subset selection formulation. The interest is focused (i) on the selection of the best population among k independent populations and (ii) on the selection of the best population, which is closest to an additional standard or control population. With respect to the first problem the populations are ranked in terms of entropies of their distributions and the population whose distribution has maximum entropy is selected. For the second problem the populations are ranked in terms of divergences between their distributions and the distribution of the standard or control population and the population with the minimum divergence is selected. In each case the populations are assumed to have general parametric densities satisfying the classical regularity conditions of asymptotic statistic. Large sample properties of the estimators of entropies and divergences of the populations will be studied and used in order to determine the probabilities of correct selection of the proposed asymptotic selection rules. Illustrative examples, including a numerical example using real medical data appeared-in the literature; will be given for multivariate homoscedastic normal populations and populations described by the regular exponential family of distributions.Item The generalized entropy measure to the design and comparison of regression experiment in a Bayesian context(Information Sciences, 1993) Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Menéndez Calleja, María Luisa; Taneja, I.J.Taneja [14] studied a unified (r, s)-entropy that includes as a particular case some of the known entropies. Based on this unified (r, s)-entropy, Pardo et al. [8] defined the average amount of information provided by an experiment X over the unknown parameter θ with prior knowledge p(θ). By using average amount of information in unified form, we compare experiments based on the Bayesian approach. Some connections with the criterion of Blackwell and Lehmann are also made. In this paper, an application of generalized entropy measures to the design and comparison of linear regression experiment is presented.Item Sufficient fuzzy information systems(Fuzzy Sets and Systems, 1989) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, LeandroIn this paper we suggest and study a new selection criterion in order to compare probabilistic information systems when the available information from them is vague, in the sense that it might be considered as fuzzy information (Tanaka, Okuda and Asai). This criterion is based on the concept of sufficient probabilistic information system established by Blackwell.Item Tests of hypotheses for and against order restrictions on multinomial parameters based on phi-divergences(Utilitas mathematica, 2002) Menéndez Calleja, María Luisa; Pardo Llorente, Leandro; Zografos, KonstantinosMeasures of phi-divergences are widely used as statistical tools for making inferences about a collection p(1), p(2),...,p(M) of multinomial parameters (Morales et al. (1995), Zografos et al. (1990), etc). Many such collections appearing in practice exhibit a trend (Robertson (1978), Lee (1987), Robertson et al. (1988) and many others cited there). In this paper tests based on measures of phi-divergence arc considered for testing a. simple null hypothesis on a. collection of multinomial parameters against an order restricted alternative and for testing an order restriction against no restriction on the collection of multinomial parameters.Item Asymptotic distributions of weighted divergence between discrete distributions(Communications in statistics. Theory and methods, 1998) Franck, Ove; Menéndez Calleja, María Luisa; Pardo Llorente, LeandroA divergence measure between discrete probability distributions introduced by Csiszar (1967) generalizes the Kullback-Leibler information and several other information measures considered in the literature. We introduce a weighted divergence which generalizes the weighted Kullback-Leibler information considered by Taneja (1985). The weighted divergence between an empirical distribution and a fixed distribution and the weighted divergence between two independent empirical distributions are here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear combination of independent chi(2)-variables.Item On tests of symmetry, marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum phi-divergence estimator with constraints(Journal of Statistical Computation and Simulation, 2005) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Zografos, KonstantinosThe restricted minimum phi-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum phi-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221-237], is employed to obtain estimates of the cell frequencies of an 1 x 1 contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated phi-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function phi(2) for estimation and the best function phi(1) for testing.Item Tests based on phi-divergences for bivariate symmetry(Metrika, 2001) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, LeandroIn this paper we introduce a family of test statistics for testing symmetry based on phi -divergcnce families. These test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. Asymptotic distribution for the new test statistics are derived under both the null and the alternative hypotheses. A simulation study is presented to see that some new test statistics offer an attractive alternative to the classical Pearson lest statistic for the problem of symmetry.