Examples And Problems In Mathematical Statistics

Provides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features: Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving More than 430 unique exercises with select solutions Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.

Approximately 1,000 problems — with answers and solutions included at the back of the book — illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

What is most valuable about this book is the very high quality of the model solutions It is a problem book for those teaching or learning a first course in mathematical statistics This one is outstandingly good and highly recommended.Goeff CohenUniversity of Edinburgh, ScotlandThe authors of this useful book take the view that the ability to solve practical problems is fundamental to an understanding of statistical techniques The book is designed to be read alongside a standard text. I expect it is likely to be most useful to the teacher or to the able student forced to work largely alone.David GreenThis book not only provides a solution to each problem set but gives notes about that solution. These notes should help students to understand the reasoning behind the techniques used, so giving them confidence to deal with problems of a similar nature This book should prove a valuable addition to the library of students and teachers of statistics.M J G AnsellHatfield PolytechnicThe book consists of aseries of examples, each followed by one or more alternative solutions and accompanying notes. The solutions themselves are useful models. The notes go one stage further and explain why particular techniques were chosen to solve each problem. This approach may help to overcome the common difficulty of deciding which method to choose when answering examination questions The book is easy to read and suitable for individual study.Richard J FieldThese notes provide fascinating insights into the process that experienced statisticians go through in order to solve a problem. Students (and maybe some instructors) will benefit greatly from going through the solutions and the notes in thisbook.Gudmund R IversenSwarthmore CollegeThe approach of the authors is to improve a students understanding of statistics, and to help students appreciate which techniques might be appropriate for any problem.Zentralblatt Math., 2001

This book contains S. S. Wilks' lessons on mathematical statistics, and will make an excellent addition to the bookshelf of anyone with an interest in the subject. Preface: 'Most of the mathematical theory of statistics in its present state has been developed during the past twenty years. Because of the variety of scientific fields in which statistical problems have arisen, the original contributions to this branch of applied mathematics are widely scattered in scientific literature. Most of the theory still exists only in original form. During the past few years the author has conducted a two-semester course at Princeton University for advanced undergraduates and beginning graduate students in which an attempt has been made to give the students an introduction to the more recent developments in the mathematical theory of statistics. The subject matter for this course has been gleaned, for the most part, from periodical literature. Since it is impossible to cover in detail any large portion of this literature in two semesters, the course has been held primarily to the basic mathematics of the material, with just enough problems and examples for illustrative and examination purposes...'

A wide-ranging, extensive overview of modern mathematical statistics, this work reflects the current state of the field while being succinct and easy to grasp. The mathematical presentation is coherent and rigorous throughout. The author presents classical results and methods that form the basis of modern statistics, and examines the foundations of estimation theory, hypothesis testing theory and statistical game theory. He then considers statistical problems for two or more samples, and those in which observations are taken from different distributions. Methods of finding optimal and asymptotically optimal statistical procedures are given, along with treatments of homogeneity testing, regression, variance analysis and pattern recognition. The author also posits a number of methodological improvements that simplify proofs, and brings together a number of new results which have never before been published in a single monograph.

Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.