Название: Mathematical Statistics with Resampling and R, 3rd EditionАвтор: Laura M. Chihara, Tim C. Hesterberg
Издательство: Wiley
Год: 2022
Страниц: 579
Язык: английский
Формат: pdf (true)
Размер: 34.5 MB
This book bridges the latest software applications with the benefits of modern resampling techniques.
Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques.
Incorporating resampling and bootstrapping methods requires that students use statistical software. We use R or RStudio because they are freely available, powerful, flexible, and a valuable tool in future careers. One of us worked at Google where there was an explosion in the use of R, with more and more non-statisticians learning R (the statisticians already know it). We realize that the learning curve for R is high, but believe that the time invested in mastering R is worth the effort. We have written some basic materials on R that are available on the website for this text. We recommend that instructors work through the introductory worksheet with the students on the first or second day of the term, in a computer lab if possible.
For the third edition, we decided to incorporate the packages in Hadley Wickham’s Tidyverse, including Ggplot2. And though some R packages exist that implement some of the bootstrap and permutation algorithms that we teach, we felt that students understand and internalize the concepts better if they are required to write the code themselves. We do provide R scripts or R Markdown files with code on our website, and we may include alternate coding using some of the many R packages available.
The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as:
Exploratory data analysis
Calculation of sampling distributions
The Central Limit Theorem
Monte Carlo sampling
Maximum likelihood estimation and properties of estimators
Confidence intervals and hypothesis tests
Regression
Bayesian methods
Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints. Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work.
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