Ayanendranath Basu - 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.

In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Statistical Inference: The Minimum Distance Approach comprehensively overviews developments in density-based minimum distance inference for independently and identically distributed data. Extensions to other more complex models are also discussed. Comprehensively covering the basics and applications of minimum distance inference, this book introduces and discusses: The estimation and hypothesis testing problems for both discrete and continuous modelsThe robustness properties and the structural geometry of the minimum distance methodsThe inlier problem and its possible solutions, and the weighted likelihood estimation problem The extension of the minimum distance methodology in interdisciplinary areas, such as neural networks and fuzzy sets, as well as specialized models and problems, including semi-parametric problems, mixture models, grouped data problems, and survival analysis. Statistical Inference: The Minimum Distance Approach gives a thorough account of density-based minimum distance methods and their use in statistical inference. It covers statistical distances, density-based minimum distance methods, discrete and continuous models, asymptotic distributions, robustness, computational issues, residual adjustment functions, graphical descriptions of robustness, penalized and combined distances, weighted likelihood, and multinomial goodness-of-fit tests. This carefully crafted resource is useful to researchers and scientists within and outside the statistics arena.

In many ways, estimation by an appropriate minimum distance method is one of the most natural ideas in statistics. However, there are many different ways of constructing an appropriate distance between the data and the model: the scope of study referred to by "Minimum Distance Estimation" is literally huge. Filling a statistical resource gap, Statistical Inference: The Minimum Distance Approach comprehensively overviews developments in density-based minimum distance inference for independently and identically distributed data. Extensions to other more complex models are also discussed. Comprehensively covering the basics and applications of minimum distance inference, this book introduces and discusses: The estimation and hypothesis testing problems for both discrete and continuous modelsThe robustness properties and the structural geometry of the minimum distance methodsThe inlier problem and its possible solutions, and the weighted likelihood estimation problem The extension of the minimum distance methodology in interdisciplinary areas, such as neural networks and fuzzy sets, as well as specialized models and problems, including semi-parametric problems, mixture models, grouped data problems, and survival analysis. Statistical Inference: The Minimum Distance Approach gives a thorough account of density-based minimum distance methods and their use in statistical inference. It covers statistical distances, density-based minimum distance methods, discrete and continuous models, asymptotic distributions, robustness, computational issues, residual adjustment functions, graphical descriptions of robustness, penalized and combined distances, weighted likelihood, and multinomial goodness-of-fit tests. This carefully crafted resource is useful to researchers and scientists within and outside the statistics arena.

A User's Guide to Business Analytics provides a comprehensive discussion of statistical methods useful to the business analyst. Methods are developed from a fairly basic level to accommodate readers who have limited training in the theory of statistics. A substantial number of case studies and numerical illustrations using the R-software package are provided for the benefit of motivated beginners who want to get a head start in analytics as well as for experts on the job who will benefit by using this text as a reference book.The book is comprised of 12 chapters. The first chapter focuses on business analytics, along with its emergence and application, and sets up a context for the whole book. The next three chapters introduce R and provide a comprehensive discussion on descriptive analytics, including numerical data summarization and visual analytics. Chapters five through seven discuss set theory, definitions and counting rules, probability, random variables, and probability distributions, with a number of business scenario examples. These chapters lay down the foundation for predictive analytics and model building.Chapter eight deals with statistical inference and discusses the most common testing procedures. Chapters nine through twelve deal entirely with predictive analytics. The chapter on regression is quite extensive, dealing with model development and model complexity from a user’s perspective. A short chapter on tree-based methods puts forth the main application areas succinctly. The chapter on data mining is a good introduction to the most common machine learning algorithms. The last chapter highlights the role of different time series models in analytics. In all the chapters, the authors showcase a number of examples and case studies and provide guidelines to users in the analytics field.

This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12–16 January, 2015. The book explores the applicability of robust methods in other non-traditional areas which includes the use of new techniques such as skew and mixture of skew distributions, scaled Bregman divergences, and  multilevel functional data methods; application areas being circular data models and prediction of mortality and life expectancy. The contributions are of both theoretical as well as applied in nature. Robust statistics is a relatively young branch of statistical sciences that is rapidly emerging as the bedrock of statistical analysis in the 21st century due to its flexible nature and wide scope. Robust statistics supports the application of parametric and other inference techniques over a broader domain than the strictly interpreted model scenarios employed in classical statistical methods.The aim of the ICORS conference, which is being organized annually since 2001, is to bring together researchers interested in robust statistics, data analysis and related areas. The conference is meant for theoretical and applied statisticians, data analysts from other fields, leading experts, junior researchers and graduate students. The ICORS meetings offer a forum for discussing recent advances and emerging ideas in statistics with a focus on robustness, and encourage informal contacts and discussions among all the participants. They also play an important role in maintaining a cohesive group of international researchers interested in robust statistics and related topics, whose interactions transcend the meetings and endure year round.

This book offers a collection of recent contributions and emerging ideas in the areas of robust statistics presented at the International Conference on Robust Statistics 2015 (ICORS 2015) held in Kolkata during 12–16 January, 2015.