Person:
Pardo Llorente, Leandro

First Name

Leandro

Last Name

Pardo Llorente

URI

https://hdl.handle.net/20.500.14352/75622

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Estadística e Investigación Operativa

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 9 of 9

An Approach to Canonical Correlation Analysis Based on Rényi’s Pseudodistances
(Entropy, 2023) Jaenada Malagón, María; Miranda Menéndez, Pedro; Pardo Llorente, Leandro; Zografos, Konstantinos
Canonical Correlation Analysis (CCA) infers a pairwise linear relationship between two groups of random variables, 𝑿 and 𝒀. In this paper, we present a new procedure based on Rényi’s pseudodistances (RP) aiming to detect linear and non-linear relationships between the two groups. RP canonical analysis (RPCCA) finds canonical coefficient vectors, 𝒂 and 𝒃, by maximizing an RP-based measure. This new family includes the Information Canonical Correlation Analysis (ICCA) as a particular case and extends the method for distances inherently robust against outliers. We provide estimating techniques for RPCCA and show the consistency of the proposed estimated canonical vectors. Further, a permutation test for determining the number of significant pairs of canonical variables is described. The robustness properties of the RPCCA are examined theoretically and empirically through a simulation study, concluding that the RPCCA presents a competitive alternative to ICCA with an added advantage in terms of robustness against outliers and data contamination.
The moment-corrected phi-divergence test statistics for symmetry
(Journal of Computational and Applied Mathematics, 2007) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro
In this paper we consider the family of phi-divergence test statistics, T-n(phi,S), for the problem of symmetry in I x I contingency tables whose asymptotic distribution is chi-square with I (I - 1)/2 degrees of freedom and we propose a moment-corrected phi-divergence test statistic in order to improve the accuracy of the chi-square approximation of the distribution of T,T-n(phi,S) under the hypothesis of symmetry.
On tests of homogeneity based on minimum phi-divergence estimator with constraints
(Computational Statistics and Data Analysis, 2003) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Zografos, Konstantinos
A family of tests of homogeneity of independent multinomial populations is introduced in terms of the phi(1)-divergence when the parameters are estimated using the minimum phi(2)-divergence estimator instead of the maximum likelihood estimator. A simulation study is presented to choose the best function phi(2) for estimation and the best function phi(1) for testing. A new test statistic is obtained, more powerful in some cases, than the existing tests for testing homogeneity in multinomial populations.
An exploratory canonical analysis approach for multinomial populations based on the phi-divergence measure
(Kybernetika, 2004) Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen; Zografos, Konstantinos
In this paper we consider an exploratory canonical analysis approach for multinomial population based on the phi-divergence measure. We define the restricted minimum phi-divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in phi-divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness of the model.
A preliminary test in classification and probabilities of misclassification
(Statistics, 2005) Menéndez, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Zografos, Konstantinos
Consider f(theta) to be a probability density function with parameter theta. A set of k populations can now be defined such that the ith population Pi(i) is the set of density functions f(theta 1(i)),...,f(theta mi(i)). This paper proposes a test, based on the Psi-dissimilariiy, of the hypothesis that a new individual from a population Pi(0) with a density function f(theta 0), belongs to the ith population. The probabilities of misclassification of the minimum Psi-dissimilarity classification rule are also obtained. In this paper, it is assumed that the parameters theta(1)((i)),...,theta(mi)((i)) and may be theta(0) are unknown and must be estimated from a set of training samples. Explicit expressions for the hypothesis test and the probabilities of misclassification are derived for the case where the populations Pi(i) consist of homoscedastic normal, as well as for gamma distributions.
A New Measure of Leverage Cells in Multinomial Loglinear Models
(Communications in statistics. Theory and methods, 2010) Martín Apaolaza, Níriam; Pardo Llorente, Leandro
In this article, a family of measures for detecting leverage cells in multinomial loglinear models based on Renyi's divergence measures is presented and its properties are studied. An example illustrates its behavior.
On tests of independence based on minimum phi-divergence estimator with constraints: An application to modeling DNA
(Computational Statistics and Data Analysis, 2006) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Zografos, Konstantinos
A new family of estimators, Minimum phi-divergence estimators, is introduced for the problem of independence in a two-way contingency table and their asymptotic properties are studied. Based on this new family of estimators, a new family of test statistics for the problem of independence is defined. This new family of test statistics yield the likelihood ratio test and the Pearson test statistic as special cases. A simulation study is presented to show that some new test statistics offer an attractive alternative to the classical Pearson and likelihood ratio test statistics for this problem. The procedures proposed in this paper can be used for testing positional independence of a DNA sequence as it is illustrated by a numerical example.
Phi-divergence statistics for testing linear hypotheses in logistic regression models
(Communications in statistics.Theory and methods, 2008) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro
In this paper we introduce and study two new families of statistics for the problem of testing linear combinations of the parameters in logistic regression models. These families are based on the phi-divergence measures. One of them includes the classical likelihood ratio statistic and the other the classical Pearson's statistic for this problem. It is interesting to note that the vector of unknown parameters, in the two new families of phi-divergence statistics considered in this paper, is estimated using the minimum phi-divergence estimator instead of the maximum likelihood estimator. Minimum phi-divergence estimators are a natural extension of the maximum likelihood estimator.
Tests for bivariate symmetry against ordered alternatives in square contingency tables
(Australian & New Zealand Journal of Statistics, 2003) Menéndez Calleja, María Luisa; Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro
Let X and Y denote two ordinal response variables, each having I levels. When subjects are classified on both variables, there are I-2 possible combinations of classifications. Let p(ij) = Pr(X = i, Y = j). This paper introduces a family of tests based on phi-divergence measures for testing H-0: p(ij) = p(ji) against H-1: p(ij) greater than or equal to p(ji) (i greater than or equal to j); and for testing H-1 against H-2: p(ij) unrestricted. A simulation study assesses some of the family of tests introduced in this paper in comparison to the likelihood ratio test.