Person: Castilla González, Elena María
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First Name
Elena María
Last Name
Castilla González
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Estadística e Investigación Operativa
Area
Estadística e Investigación Operativa
Identifiers
17 results
Search Results
Now showing 1 - 10 of 17
Item 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, KonstantinosThis 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.Item Robust inference for non-destructive one-shot device testing under step-stress model with exponential lifetimes(2022) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Jaenada Malagón, María; Pardo Llorente, LeandroOne-shot devices analysis involves an extreme case of interval censoring, wherein one can only know whether the failure time is either before or after the test time. Some kind of one-shot devices do not get destroyed when tested, and so can continue within the experiment, providing extra information for inference, if they did not fail before an inspection time. In addition, their reliability can be rapidly estimated via accelerated life tests (ALTs) by running the tests at varying and higher stress levels than working conditions. In particular, step-stress tests allow the experimenter to increase the stress levels at pre-fixed times gradually during the life-testing experiment. The cumulative exposure model is commonly assumed for step-stress models, relating the lifetime distribution of units at one stress level to the lifetime distributions at preceding stress levels. In this paper, we develop robust estimators and Z-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 distribution. We study asymptotic and robustness properties of the estimators and test statistics, yielding point estimation and conffidence intervals for different lifetime characteristic such as reliability, distribution quantiles and mean lifetime of the devices. A simulation study is carried out to assess the performance of the methods of inference developed here and some real-life data sets are analyzed ffinally for illustrative purpose.Item Robust semiparametric inference for polytomous logistic regression with complex survey design(Advances in Data Analysis and Classification, 2020) Castilla González, Elena María; Ghosh, Abhik; Martín Apaolaza, Nirian; Pardo Llorente, LeandroAnalyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for the polytomous logistic regression model with such a complex survey. This family of semiparametric estimators is a robust generalization of the maximum quasi weighted likelihood estimator exploiting the advantages of the popular density power divergence measure. Accordingly robust estimators for the design effects are also derived. Using the new estimators, robust testing of general linear hypotheses on the regression coefficients are proposed. Their asymptotic distributions and robustness properties are theoretically studied and also empirically validated through a numerical example and an extensive Monte Carlo studyItem Robust statistical inference for one-shot devices based on divergences(2021) Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroA one-shot device is a unit that performs its function only once and, after use, the device either gets destroyed or must be rebuilt. For this kind of device, one can only know whether the failure time is either before or after a speci c inspection time, and consequently the lifetimes are either left- or right-censored, with the lifetime being less than the inspection time if the test outcome is a failure (resulting in left censoring) and the lifetime being more than the inspection time if the test outcome is a success (resulting in right censoring). An accelerated life test (ALT) plan is usually employed to evaluate the reliability of such products by increasing the levels of stress factors and then extrapolating the life characteristics from high stress conditions to normal operating conditions. This acceleration process will shorten the life span of devices and reduce the costs associated with the experiment. The study of one-shot device from ALT data has been developed considerably recently, mainly motivated by the work of Fan et al. [2009]...Item 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, LeandroSince 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.Item Robust Inference for One-Shot Device Testing Data Under Weibull Lifetime Model(IEEE Transactions on Reliability, 2020) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, LeandroClassical inferential methods for one-shot device testing data from an accelerated life-test are based on maximum likelihood estimators (MLEs) of model parameters. However, the lack of robustness of MLE is well-known. In this article, we develop robust estimators for one-shot device testing by assuming a Weibull distribution as a lifetime model. Wald-type tests based on these estimators are also developed. Their robustness properties are evaluated both theoretically and empirically, through an extensive simulation study. Finally, the methods of inference proposed are applied to three numerical examples. Results obtained from both Monte Carlo simulations and numerical studies show the proposed estimators to be a robust alternative to MLEs.- Project number: 166
Item Tutorial interactivo de ejemplos básicos y ejercicios de inferencia estadística no-paramétrica mediante software libre: implementación mediante R, R-studio y Swirl(2019) Martín Apaolaza, Nirian; Castilla González, Elena María; Miranda Menéndez, Pedro; Pardo Llorente, Leandro - Project number: 343
Item Tutoriales guiados de prácticas en “Estadística: Análisis de Datos e Inferencia” mediante el software libre SAS University Edition(2020) Martín Apaolaza, Nirian; Castilla González, Elena María; Chocano Feito, Pedro José; Jaenada Malagón, María; Pardo Llorente, Leandro Item 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, LeandroIn 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.Item Enseñanza del Software Estadístico R a alumnos de Matemáticas(Pensamiento Matemático, 2021) Castilla González, Elena María; Chocano Feito, Pedro JoséHabiendo constatado la falta de formación en herramientas estadísticas en algunas titulaciones de matemáticas, así como la creciente importancia del software de programación R, se ha visto la necesidad de impartir un curso de Análisis de Datos con R. Éste se ha desarrollado dentro de la iniciativa “Compumates” de la Facultad de CC. Matemáticas, Universidad Complutense de Madrid, y ha constado de diferentes sesiones, que parten desde la instalación del software y uso de comandos básicos, hasta su aplicación en técnicas de análisis y predicción. Para ello se ha provisto a los alumnos de un manual de aprendizaje. En este trabajo se muestran los resultados que ha tenido la experiencia en el aprendizaje del alumno y la valoración que tiene éste sobre la misma.