Examples in Parametric Inference with R

This book discusses examples in parametric inference with R. Combining basic theory with modern approaches, it presents the latest developments and trends in statistical inference for students who do not have an advanced mathematical and statistical background. The topics discussed in the book are fundamental and common to many fields of statistical inference and thus serve as a point of departure for in-depth study. The book is divided into eight chapters: Chapter 1 provides an overview of topics on sufficiency and completeness, while Chapter 2 briefly discusses unbiased estimation. Chapter 3 focuses on the study of moments and maximum likelihood estimators, and Chapter 4 presents bounds for the variance. In Chapter 5, topics on consistent estimator are discussed. Chapter 6 discusses Bayes, while Chapter 7 studies some more powerful tests. Lastly, Chapter 8 examines unbiased and other tests.

Senior undergraduate and graduate students in statistics and mathematics, and thosewho have taken an introductory course in probability, will greatly benefit from this book. Students are expected to know matrix algebra, calculus, probability and distribution theory before beginning this course. Presenting a wealth of relevant solved and unsolved problems, the book offers an excellent tool for teachers and instructors who can assign homework problems from the exercises, and students will find the solved examples hugely beneficial in solving the exercise problems.

“The author has created a unique text about classical mathematical statistics which is distinguished by its example-based explanations of concepts and comparatively simple proofs of key results. … this is a unique contribution, with a nice collection of worked examples that should be helpful to students seeking to bridge the gap between example-sparse theoretical texts and mathematically inadequate applied texts.” (Todd Alan Kuffner, Mathematical Reviews, August, 2017)

Ulhas Jayram Dixit is Professor, at the Department of Statistics, University of Mumbai, India. He is the first Rothamsted International Fellow at Rothamsted Experimental Station in the UK, which is the world’s oldest statistics department. Further, he received the Sesqui Centennial Excellence Award in research and teaching from the University of Mumbai in 2008. He is member of the New Zealand Statistical Association, the Indian Society for Probability and Statistics, Bombay Mathematical Colloquium, and the Indian Association for Productivity, Quality and Reliability. Editor of Statistical Inference and Design of Experiment (published by Narosa), Prof. Dixit has published over 40 papers in several international journals of repute. His topics of interest are outliers, measure theory, distribution theory, estimation, elements of stochastic process, non-parametric inference, stochastic process, linear models, queuing and information theory, multivariate analysis, financial mathematics, statistical methods, design of experiments, and testing of hypothesis. He received his Ph.D. degree from the University of Mumbai in 1989.