Statistical Inference based on the Density Power Divergence by Basu, Ayanendranath; Ghosh, Abhik; Pardo, Leandro;

Short description:

All scientists, researchers and data analysts, who have to handle real data as part of their scientific explorations, have, from time to time, to face to the problem of having to deal with data which do not exactly conform to the model which was expected to describe these data.

Long description:

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 them

Statistical 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.

Table of Contents:

1. Introduction  2. The Density Power Divergence  3. Parametric Stochastic Regression Models 4. Inference for Independent Non-Homogeneous Data  5. The DPD in Time Series Analysis  6. Robust Model and Variable Selection  7. Inference in Mixture Models  8. Robust Survival Analysis 9. Inference for Stochastic Processes  10. DPD-based Robust Pseudo-Bayes Estimation  11. The Logarithmic DPD and Other Extensions