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 24

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.
Minimum ϕ-Divergence Estimation in Constrained Latent Class Models for Binary Data
(Psychometrika, 2015) Felipe Ortega, Ángel; Miranda Menéndez, Pedro; Pardo Llorente, Leandro
The main purpose of this paper is to introduce and study the behavior of minimum (Formula presented.)-divergence estimators as an alternative to the maximum-likelihood estimator in latent class models for binary items. As it will become clear below, minimum (Formula presented.)-divergence estimators are a natural extension of the maximum-likelihood estimator. The asymptotic properties of minimum (Formula presented.)-divergence estimators for latent class models for binary data are developed. Finally, to compare the efficiency and robustness of these new estimators with that obtained through maximum likelihood when the sample size is not big enough to apply the asymptotic results, we have carried out a simulation study.
Empirical phi-divergence test statistics for testing simple and composite null hypotheses
(Statistics: A Journal of Theoretical and Applied Statistics, 2015) Balakrishnan, Narayanaswamy; Martin, Nirian; Pardo Llorente, Leandro
The main purpose of this paper is to introduce first a new family of empirical test statistics for testing a simple null hypothesis when the vector of parameters of interest is defined through a specific set of unbiased estimating functions. This family of test statistics is based on a distance between two probability vectors, with the first probability vector obtained by maximizing the empirical likelihood (EL) on the vector of parameters, and the second vector defined from the fixed vector of parameters under the simple null hypothesis. The distance considered for this purpose is the phi-divergence measure. The asymptotic distribution is then derived for this family of test statistics. The proposed methodology is illustrated through the well-known data of Newcomb's measurements on the passage time for light. A simulation study is carried out to compare its performance with that of the EL ratio test when confidence intervals are constructed based on the respective statistics for small sample sizes. The results suggest that the empirical modified likelihood ratio test statistic' provides a competitive alternative to the EL ratio test statistic, and is also more robust than the EL ratio test statistic in the presence of contamination in the data. Finally, we propose empirical phi-divergence test statistics for testing a composite null hypothesis and present some asymptotic as well as simulation results for evaluating the performance of these test procedures.
Restricted distance-type Gaussian estimators based on density power divergence and their aplications in hypothesis testing
(Mathematics, 2023) Felipe Ortega, Ángel; Jaenada Malagón, María; Miranda Menéndez, Pedro; Pardo Llorente, Leandro
In this paper, we introduce the restricted minimum density power divergence Gaussian estimator (MDPDGE) and study its main asymptotic properties. In addition, we examine it robustness through its influence function analysis. Restricted estimators are required in many practical situations, such as testing composite null hypotheses, and we provide in this case constrained estimators to inherent restrictions of the underlying distribution. Furthermore, we derive robust Rao-type test statistics based on the MDPDGE for testing a simple null hypothesis, and we deduce explicit expressions for some main important distributions. Finally, we empirically evaluate the efficiency and robustness of the method through a simulation study
Robust approach for comparing two dependent normal populations through Wald-type tests based on Rényi's pseudodistance estimators
(Statistics and Computing, 2022) Castilla González, Elena María; Jaenada Malagón, María; Martín Apaolaza, Nirian; Pardo Llorente, Leandro
Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and other tests, focused on paired correlated normal random samples, Rényi's pseudodistance estimators are proposed, their asymptotic distribution is established and an iterative algorithm is provided for their computation. From them the Wald-type test statistics are constructed for different problems of interest and their influence function is theoretically studied. For testing null correlation in different contexts, an extensive simulation study and two real data based examples support the robust properties of our proposal.
Robust adaptive Lasso in high-dimensional logistic regression with an application to genomic classification of cancer patients
(2021) Basu, A.; Ghosh, A.; Jaenada Malagón, María; Pardo Llorente, Leandro
Penalized logistic regression is extremely useful for binary classiffication with a large number of covariates (significantly higher than the sample size), having several real life applications, including genomic disease classification. However, the existing methods based on the likelihood based loss function are sensitive to data contamination and other noise and, hence, robust methods are needed for stable and more accurate inference. In this paper, we propose a family of robust estimators for sparse logistic models utilizing the popular density power divergence based loss function and the general adaptively weighted LASSO penalties. We study the local robustness of the proposed estimators through its in uence function and also derive its oracle properties and asymptotic distribution. With extensive empirical illustrations, we clearly demonstrate the significantly improved performance of our proposed estimators over the existing ones with particular gain in robustness. Our proposal is finally applied to analyse four different real datasets for cancer classification, obtaining robust and accurate models, that simultaneously performs gene selection and patient classification.
Classification of COVID19 Patients Using Robust Logistic Regression
(Journal of Statistical Theory and Practice, 2022) Ghosh, Abhik; Jaenada Malagón, María; Pardo Llorente, Leandro
Coronavirus disease 2019 (COVID19) has triggered a global pandemic affecting millions of people. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) causing the COVID-19 disease is hypothesized to gain entry into humans via the airway epithelium, where it initiates a host response. The expression levels of genes at the upper airway that interact with the SARS-CoV-2 could be a telltale sign of virus infection. However, gene expression data have been flagged as suspicious of containing different contamination errors via techniques for extracting such information, and clinical diagnosis may contain labelling errors due to the specificity and sensitivity of diagnostic tests. We propose to fit the regularized logistic regression model as a classifier for COVID-19 diagnosis, which simultaneously identifies genes related to the disease and predicts the COVID-19 cases based on the expression values of the selected genes. We apply a robust estimating methods based on the density power divergence to obtain stable results ignoring the effects of contamination or labelling errors in the data and compare its performance with respect to the classical maximum likelihood estimator with different penalties, including the LASSO and the general adaptive LASSO penalties.
Minimum phi-divergence estimators with constraints in multinomial populations
(Journal of Statistical Planning and Inference, 2002) Pardo Llorente, Julio Ángel; Pardo Llorente, Leandro; Zografos, Konstantinos
This paper presents a minimum phi-divergence estimation procedure in multinomial models in which the probabilities depend on unknown parameters that are not mathematically independent but satisfy some functional relationships, This estimator is then used in a phi-divergence statistic for solving the problem of goodness-of-fit when the unknown parameters in the probabilities are not mathematically independent. The asymptotic distribution of this family of statistics is obtained under the null and contiguous alternative hypotheses, The asymptotic distribution of residuals. when the parameters are estimated using the minimum phi-divergence estimator. is also obtained.
Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances
(IEEE transactions on information theory, 2022) Castilla González, Elena María; Jaenada Malagón, María; Pardo Llorente, Leandro
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) with non-random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to small deviations from the assumed conditions. In this paper, and based on the Rényi’s pseudodistance (RP), we introduce a new family of estimators in case our information about the unknown parameter is given for i.n.i.d.o.. This family of estimators, let us say minimum RP estimators (as they are obtained by minimizing the RP between the assumed distribution and the empirical distribution of the data), contains the MLE as a particular case and can be applied, among others, to the MLRM with non-random covariates. Based on these estimators, we introduce Wald-type tests for testing simple and composite null hypotheses, as an extension of the classical MLE-based Wald test. Influence functions for the estimators and Wald-type tests are also obtained and analysed. Finally, a simulation study is developed in order to asses the performance of the proposed methods and some real-life data are analysed for illustrative purpose.
Robust Rao-type tests for non-destructive one-shot device testing under step-stress model with exponential lifetimes
(2022) Balakrishnan, Narayanaswamy; Jaenada Malagón, María; Pardo Llorente, Leandro
One-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is before the test time. Some kind of one-shot units do not get destroyed when tested, and then survival units can continue within the test providing extra information for inference. This not-destructiveness is a great advantage when the number of units under test are few. On the other hand, one-shot devices may last for long times under normal operating conditions and so accelerated life tests (ALTs), which increases the stress levels at which units are tested, may be needed. ALTs relate the lifetime distribution of an unit with the stress level at which it is tested via log-linear relationship, so inference results can be easily extrapolated to normal operating conditions. In particular, the step-stress model, which allows the experimenter to increase the stress level at pre-fixed times gradually during the life-testing experiment is specially advantageous for non-destructive one-shot devices. In this paper, we develop robust Rao-type test statistics based on the density power divergence (DPD) for testing linear null hypothesis for non-destructive one-shot devices under the step-stress ALTs with exponential lifetime distributions. We theoretically study their asymptotic and robustness properties, and empirically illustrates such properties through a simulation study.