The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical maximum likelihood based techniques. Recently Ghosh et al. (2013) proposed a general class of divergence measures for robust statistical inference, named the S-Divergence Family. Ghosh (2014) discussed its asymptotic properties for the discrete model of densities. In the present paper, we develop the asymptotic properties of the proposed minimum S-Divergence estimators under continuous models. Here we use the Basu-Lindsay approach (1994) of smoothing the model densities that, unlike previous approaches, avoids much of the complications of the kernel bandwidth selection. Illustrations are presented to support the performance of the resulting estimators both in terms of efficiency and robustness through extensive simulation studies and real data examples.Comment: Pre-Print, 34 page

Inferencia estadística robusta basada en divergencias para dispositivos de un sólo uso

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 30-06-2021A 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]...Los dispositivos de un solo uso (one shot devices en ingles), son aquellos que, una vez usados, dejan de funcionar. La mayor dificultad a la hora de modelizar su tiempo de vida es que solo se puede saber si el momento de fallo se produce antes o despues de un momento específico de inspeccion. As pues, se trata de un caso extremo de censura intervalica: si el tiempo de vida es inferior al de inspeccion observaremos un fallo (censura por la izquierda), mientras que si el tiempo de vida es mayor que el tiempo de inspeccion, observaremos un exito (censura por la derecha). Para la observacion y modelizacion de este tipo de dispositivos es comun el uso de tests de vida acelerados. Los tests de vida acelerados permiten evaluar la fiabilidad de los productos en menos tiempo, incrementando las condiciones a las que se ven sometidos los dispositivos para extrapolar despues estos resultados a condiciones mas normales. El estudio de los dispositivos de un solo uso por medio de tests de vida acelerados se ha incrementado considerablemente en los ultimos a~nos motivado, principalmente, por el trabajo de Fan et al. [2009]...Fac. de Ciencias MatemáticasTRUEunpu

Robust Procedures for Estimating and Testing in the Framework of Divergence Measures

The scope of the contributions to this book will be to present new and original research papers based on MPHIE, MHD, and MDPDE, as well as test statistics based on these estimators from a theoretical and applied point of view in different statistical problems with special emphasis on robustness. Manuscripts given solutions to different statistical problems as model selection criteria based on divergence measures or in statistics for high-dimensional data with divergence measures as loss function are considered. Reviews making emphasis in the most recent state-of-the art in relation to the solution of statistical problems base on divergence measures are also presented

Comparative Analysis of Student Learning: Technical, Methodological and Result Assessing of PISA-OECD and INVALSI-Italian Systems .

PISA is the most extensive international survey promoted by the OECD in the field of education, which measures the skills of fifteen-year-old students from more than 80 participating countries every three years. INVALSI are written tests carried out every year by all Italian students in some key moments of the school cycle, to evaluate the levels of some fundamental skills in Italian, Mathematics and English. Our comparison is made up to 2018, the last year of the PISA-OECD survey, even if INVALSI was carried out for the last edition in 2022. Our analysis focuses attention on the common part of the reference populations, which are the 15-year-old students of the 2nd class of secondary schools of II degree, where both sources give a similar picture of the students

Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences