Leandro Pardo - Böcker

All scientists, researchers, and data analysts, who handle real data as part of their scientific explorations, have had, from time to time, to face to the problem of dealing with data which do not exactly conform to the model which was expected to describe these data. Often such non-conformity is manifested through outliers. Classical techniques, which are usually optimal for "pure" data, generally have poor resistance to "noisy" data consisting of outliers or exhibiting other forms of model misspecification. This book discusses a particular method of inference which employs a robust minimum distance approach for noisy data.• Provides all the up-to-date details about a very popular robust inference method based on the density power divergence within one cover• Covers the general theory as well as applications to special types of data like survival data, count data, binary data, time series data, Markov dependent data, and many more• Discusses the problem of Bayesian robustness against data contamination • Guides the readers for practical use of this popular robust inference method through several real-life examples along with their implementation in the statistical software R (available from the author's website)• Contains many open problems in this popular research area of robust inferences, which will help the readers to choose their new research problems and enrich the field by solving themStatistical Inference based on the Denisty Power Divergence is aimed primarily at advanced graduate students, research scholars, and scientists working on robust statistical methods. Researchers from several applied fields (like biology, economics, medical sciences, sociology, business and finance, etc.) who need to analyse their experimental data with some potential noises and outliers will also find this book useful.

The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this powerful approach.Statistical Inference Based on Divergence Measures explores classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence. The first two chapters form an overview, from a statistical perspective, of the most important measures of entropy and divergence and study their properties. The author then examines the statistical analysis of discrete multivariate data with emphasis is on problems in contingency tables and loglinear models using phi-divergence test statistics as well as minimum phi-divergence estimators. The final chapter looks at testing in general populations, presenting the interesting possibility of introducing alternative test statistics to classical ones like Wald, Rao, and likelihood ratio. Each chapter concludes with exercises that clarify the theoretical results and present additional results that complement the main discussions.Clear, comprehensive, and logically developed, this book offers a unique opportunity to gain not only a new perspective on some standard statistics problems, but the tools to put it into practice.

The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this powerful approach.Statistical Inference Based on Divergence Measures explores classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence. The first two chapters form an overview, from a statistical perspective, of the most important measures of entropy and divergence and study their properties. The author then examines the statistical analysis of discrete multivariate data with emphasis is on problems in contingency tables and loglinear models using phi-divergence test statistics as well as minimum phi-divergence estimators. The final chapter looks at testing in general populations, presenting the interesting possibility of introducing alternative test statistics to classical ones like Wald, Rao, and likelihood ratio. Each chapter concludes with exercises that clarify the theoretical results and present additional results that complement the main discussions.Clear, comprehensive, and logically developed, this book offers a unique opportunity to gain not only a new perspective on some standard statistics problems, but the tools to put it into practice.

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately.This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.