Rengarajan holds a Master of Financial Engineering - University of
California, Berkeley and he works in the investment management
industry and specializes in providing economic and investment outlook
and strategy for global equity and government bond markets. He has an
educational background in financial engineering, business, and
engineering, and professional interests include business,
finance, economics, technology and related areas.
Authors: Laura Chihara & Tim Hesterberg
Students of statistics often find concepts such as sampling distributions, p-values, hypothesis test and confidence interval a bit difficult to internalize. Mathematical Statistics with Resampling and R aims to demonstrate these concepts by resampling and to apply resampling techniques to mathematical statistics.
The book is targeted towards upper undergraduate and graduate students. The emphasis of the book is on modern resampling techniques including permutation tests and bootstrapping. These techniques are introduced even before classical inference methods are discussed which helps in understanding basic statistical concepts better.
There is a discussion of several statistical case studies followed by discussion of basic concepts and definitions. Elementary data analysis is covered with an emphasis on plots, summary statistics, box plots and empirical cumulative distributive functions.
The book aims for a balance between theory, computing and application. There are numerous case studies from diverse fields through the book which illustrate real world applications of the techniques. Apart from covering the theory clearly, the book employs “R notes” to show a series of examples in R on implementing the concepts.
While discussing hypothesis testing, the book covers assumptions and implementation issues with permutation tests, test of homogeneity, and goodness of fit with all parameters are known and when some are estimated. The section on sampling distribution discusses computation/estimation, central limit theorem, and central limit theorem for binomial data.
Bootstrapping section deals with estimating the bootstrapping function, how well the bootstrapping distribution approximates the sampling distribution, and two sample bootstraps. The section ends with practical issues such as bias and accuracy of bootstrapping distributions.
Estimation discusses a very general method using maximum likelihood estimate both for discrete and continuous cases, method of moments, and properties of estimators. R Note is used to demonstrate implementation of the concepts.
Classical inference is covered in the latter part of the book including standard topics like confidence intervals for means and proportions, bootstrap, hypothesis testing for means and proportions, type 1 & type 2 errors, and likelihood ratio tests. The section on regression covers least square regression, simple linear model, and resampling correlation and regression.
The book concludes with additional topics including smoothed bootstrapping, parametric bootstrap, stretched sampling, importance sampling, and Markov Chain integration. Review of probability and probability distributions collects definitions and theorems of important probability distributions as background.
Mathematical Statistics with Resampling and R is a great resource for intermediate and advanced statistics students who want to achieve an in depth understanding of re-sampling techniques backed by practical implementation.
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