Person:
Castilla González, Elena María

First Name

Elena María

Last Name

Castilla González

URI

https://hdl.handle.net/20.500.14352/75718

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 17

Enseñanza del Software Estadístico R a alumnos de Matemáticas
(Pensamiento Matemático, 2021) Castilla González, Elena María; Chocano Feito, Pedro José
Habiendo 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.
Estadística multivariante aplicada al análisis y predicción de partidos de fútbol en las principales ligas europeas
(Pensamiento Matemático, 2021) Chocano Feito, Pedro José; Castilla González, Elena María
El propósito de este estudio es analizar las estadísticas de juego en las principales ligas europeas y ver qué factores son más determinantes a la hora de predecir el resultado de un partido. Para ello usaremos técnicas de estadística multivariante incluyendo análisis de componentes principales y regresión logística. Las dos primeras componentes principales explican alrededor del 70 % de precisión obtenida cuando se predicen victorias fuera de casa tomando como variables predictivas las propias componentes. Este estudio también demuestra que en la liga inglesa los partidos son menos equilibrados.
Optimal designs of constant‐stress accelerated life‐tests for one‐shot devices with model misspecification analysis
(Quality and Reliability Engineering International, 2021) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Ling, Man Ho
The design of constant-stress accelerated life-test (CSALT) is important in reliability estimation. In reliability studies, practitioners usually rely on underlying distribution to design CSALTs. However, model misspecification analysis of optimal designs has not been examined extensively. This paper considers one-shot device testing data by assuming gamma, Weibull, lognormal and Birnbaum–Saunders (BS) lifetime distributions, which are popular lifetime distributions in reliability studies. We then investigate the effect of model misspecification between these lifetime distributions in the design of optimal CSALTs, in which the asymptotic variance of the estimate of reliability of the device at a specific mission time is minimized subject to a prefixed budget and a termination time of the life-test. The inspection frequency, number of inspections at each stress level, and allocation of the test devices are determined in optimal design for one-shot device testing. Finally, a numerical example involving a grease-based magnetorheological fluids (G-MRF) data set is used to illustrate the developed methods. Results suggest the assumption of lifetime distribution as Weibull or lognormal to be more robust to model misspecification, while the assumption of gamma lifetime distribution seems to be the most non-robust (or most sensitive) one.
Power divergence approach for one-shot device testing under competing risks
(Journal of Computational and Applied Mathematics, 2022) Balakrishnan, Narayanaswamy; Castilla González, Elena María; Martín Apaolaza, Nirian; Pardo Llorente, Leandro
Most work on one-shot devices assume that there is only one possible cause of device failure. However, in practice, it is often the case that the products under study can experience any one of various possible causes of failure. Robust estimators and Wald-type tests are developed here for the case of one-shot devices under competing risks. An extensive simulation study illustrates the robustness of these divergence-based estimators and test procedures based on them. A data-driven procedure is proposed for choosing the optimal estimator for any given data set which is then applied to an example in the context of survival analysis.
Project number: 343
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
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.
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, Leandro
Classical 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.
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, Leandro
Analyzing 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 study
Project number: 118
Docencia de optimización en el entorno virtual Moodle a partir de ejercicios resueltos
(2022) Miranda Menéndez, Pedro; Castilla González, Elena María; Chocano Feito, Pedro José; Jaenada Malagón, María; Martín Apaolaza, Nirian; Martínez Suárez, Susana; Pardo Llorente, Leandro
El presente proyecto trata de mejorar las herramientas que tienen a su disposición los alumnos en el aprendizaje de la asignatura de Optimización. Uno de los problemas a los que se enfrentan los alumnos de esta asignatura es la escasez de bibliografía explícita referente a estos temas. Al ser ya una asignatura muy específica de los estudios de Matemáticas, no hay libros generales que traten estos temas. Por ello, los alumnos están obligados a utilizar un grupo muy reducido de libros de texto. Además, aunque en estos libros se tratan los aspectos teóricos de la asignatura, no contienen una selección de problemas resueltos que permitan a los alumnos evaluar su dominio sobre los algoritmos que aparecen en esta asignatura. Por otra parte, el entorno exam de R se ha desarrollado mucho en los últimos años. En la versión anterior, se podían generar ejercicios de forma aleatoria y a continuación producir un fichero .pdf para su impresión, pensando todavía en un uso en papel. Con la nueva versión del paquete exam todo lo anterior sigue siendo posible pero además permite que estos programas se puedan adecuar a las herramientas online, permitiendo su inclusión como una herramienta en los entornos de enseñanza virtual como Moodle. El objetivo principal de este proyecto es cubrir estas necesidades, de forma que los alumnos cuenten con una herramienta que les permita ejercitarse y profundizar en los aspectos metodológicos de la asignatura a partir de problemas resueltos.
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, Leandro
One-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.