An Introduction to Statistical Inference and Its Applications with R

An Introduction to Statistical Inference and Its Applications with R
Author: Michael W. Trosset
Publisher: CRC Press
Total Pages: 496
Release: 2009-06-23
Genre: Mathematics
ISBN: 1584889489

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Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures

Statistical Inference

Statistical Inference
Author: George Casella
Publisher: CRC Press
Total Pages: 1746
Release: 2024-05-23
Genre: Mathematics
ISBN: 1040024025

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This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and natural extensions, and consequences, of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in a lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes an extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It also stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less focused on formal optimality considerations. This is a reprint of the second edition originally published by Cengage Learning, Inc. in 2001.

Linear Statistical Inference and its Applications

Linear Statistical Inference and its Applications
Author: C. Radhakrishna Rao
Publisher: John Wiley & Sons
Total Pages: 656
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317140

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"C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran "[C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training.

The Elements of Statistical Learning

The Elements of Statistical Learning
Author: Trevor Hastie
Publisher: Springer Science & Business Media
Total Pages: 545
Release: 2013-11-11
Genre: Mathematics
ISBN: 0387216065

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During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book’s coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for “wide” data (p bigger than n), including multiple testing and false discovery rates. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.

Introduction to the Theory of Statistical Inference

Introduction to the Theory of Statistical Inference
Author: Hannelore Liero
Publisher: CRC Press
Total Pages: 280
Release: 2016-04-19
Genre: Mathematics
ISBN: 1466503203

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Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

Statistical Inference

Statistical Inference
Author: Michael J. Panik
Publisher: John Wiley & Sons
Total Pages: 294
Release: 2012-06-06
Genre: Mathematics
ISBN: 1118309804

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A concise, easily accessible introduction to descriptive and inferential techniques Statistical Inference: A Short Course offers a concise presentation of the essentials of basic statistics for readers seeking to acquire a working knowledge of statistical concepts, measures, and procedures. The author conducts tests on the assumption of randomness and normality, provides nonparametric methods when parametric approaches might not work. The book also explores how to determine a confidence interval for a population median while also providing coverage of ratio estimation, randomness, and causality. To ensure a thorough understanding of all key concepts, Statistical Inference provides numerous examples and solutions along with complete and precise answers to many fundamental questions, including: How do we determine that a given dataset is actually a random sample? With what level of precision and reliability can a population sample be estimated? How are probabilities determined and are they the same thing as odds? How can we predict the level of one variable from that of another? What is the strength of the relationship between two variables? The book is organized to present fundamental statistical concepts first, with later chapters exploring more advanced topics and additional statistical tests such as Distributional Hypotheses, Multinomial Chi-Square Statistics, and the Chi-Square Distribution. Each chapter includes appendices and exercises, allowing readers to test their comprehension of the presented material. Statistical Inference: A Short Course is an excellent book for courses on probability, mathematical statistics, and statistical inference at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for researchers and practitioners who would like to develop further insights into essential statistical tools.

A First Course in Statistical Inference

A First Course in Statistical Inference
Author: Jonathan Gillard
Publisher: Springer Nature
Total Pages: 167
Release: 2020-04-20
Genre: Mathematics
ISBN: 3030395618

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This book offers a modern and accessible introduction to Statistical Inference, the science of inferring key information from data. Aimed at beginning undergraduate students in mathematics, it presents the concepts underpinning frequentist statistical theory. Written in a conversational and informal style, this concise text concentrates on ideas and concepts, with key theorems stated and proved. Detailed worked examples are included and each chapter ends with a set of exercises, with full solutions given at the back of the book. Examples using R are provided throughout the book, with a brief guide to the software included. Topics covered in the book include: sampling distributions, properties of estimators, confidence intervals, hypothesis testing, ANOVA, and fitting a straight line to paired data. Based on the author’s extensive teaching experience, the material of the book has been honed by student feedback for over a decade. Assuming only some familiarity with elementary probability, this textbook has been devised for a one semester first course in statistics.