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 - 10 of 132

Nonadditivity in loglinear models using phi-divergences and MLEs
(Journal of Statistical Planning and Inference, 2005) Pardo Llorente, Leandro; Pardo Llorente, María del Carmen
In this paper three families of test statistics for testing nonadditivity in loglinear models are presented under the assumption of either Poisson, multinomial, or product-multinomial sampling. These new families are based on the phi-divergence measures. The standard method for testing nonadditivity is used, i.e., the two-stage tests procedure. In this procedure the parameters are first estimated using an additive model and then the estimates are treated as known constants for the second stage of the procedure. These test statistics, which are asymptotically chi-squared, generalize the likelihood ratio test for this problem given by Christensen and Utts (J. Statist. Plann. Inference 33 (1992) 333). An example and a simulation study are included.
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.
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, Leandro
In 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.
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, Igor
For 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.
Divergence-based confidence intervals in false-positive misclassification model
(Journal of Statistical Computation and Simulation, 2008) Martín Apaolaza, Níriam; Morales González, Domingo; Pardo Llorente, Leandro
In this article, we introduce minimum divergence estimators of parameters of a binary response model when data are subject to false-positive misclassification and obtained using a double-sampling plan. Under this set up, the problem of goodness-of-fit is considered and divergence-based confidence intervals (CIs) for a population proportion parameter are derived. A simulation experiment is carried out to compare the coverage probabilities of the new CIs. An application to real data is also given.
Fitting DNA sequences through log-linear modelling with linear constraints
(Statistics, 2011) Martín Apaolaza, Níriam; Pardo Llorente, Leandro
For some discrete state series, such as DNA sequences, it can often be postulated that its probabilistic behaviour is given by a Markov chain. For making the decision on whether or not an uncharacterized piece of DNA is part of the coding region of a gene, under the Markovian assumption, there are two statistical tools that are essential to be considered: the hypothesis testing of the order in a Markov chain and the estimators of transition probabilities. In order to improve the traditional statistical procedures for both of them when stationarity assumption can be considered, a new version for understanding the homogeneity hypothesis is proposed so that log-linear modelling is applied for conditional independence jointly with homogeneity restrictions on the expected means of transition counts in the sequence. In addition we can consider a variety of test-statistics and estimators by using phi-divergence measures. As special case of them the well-known likelihood ratio test-statistics and maximum-likelihood estimators are obtained.
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 Carmen
The 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.
Minimum phi-divergence estimator in logistic regression models
(Statistical Papers, 2006) Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Pardo Llorente, María del Carmen
A general class of minimum distance estimators for logistic regression models based on the phi- divergence measures is introduced: The minimum phi- divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. Its asymptotic properties are studied as well as its behaviour in small samples through a simulation study.
Model Selection in a Composite Likelihood Framework Based on Density Power Divergence
(Entropy, 2020) Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, Leandro; Zografos, Konstantinos
This paper presents a model selection criterion in a composite likelihood framework based on density power divergence measures and in the composite minimum density power divergence estimators, which depends on an tuning parameter α. After introducing such a criterion, some asymptotic properties are established. We present a simulation study and two numerical examples in order to point out the robustness properties of the introduced model selection criterion.
Minimum Phi-divergence estimators for loglinear models with linear constraints and multinomial sampling
(Statistical Papers, 2008) Martín Apaolaza, Níriam; Pardo Llorente, Leandro
In this paper the family of phi-divergence estimators for loglinear models with linear constraints and multinomial sampling is studied. This family is an extension of the maximum likelihood estimator studied by Haber and Brown (1986). A simulation study is presented and some alternative estimators to the maximum likelihood are obtained.