Book description
Advanced Statistics with Applications in R fills the gap between several excellent theoretical statistics textbooks and many applied statistics books where teaching reduces to using existing packages. This book looks at what is under the hood. Many statistics issues including the recent crisis with pvalue are caused by misunderstanding of statistical concepts due to poor theoretical background of practitioners and applied statisticians. This book is the product of a fortyyear experience in teaching of probability and statistics and their applications for solving reallife problems.
There are more than 442 examples in the book: basically every probability or statistics concept is illustrated with an example accompanied with an R code. Many examples, such as Who said π? What team is better? The fall of the Roman empire, James Bond chase problem, Black Friday shopping, Free fall equation: Aristotle or Galilei, and many others are intriguing. These examples cover biostatistics, finance, physics and engineering, text and image analysis, epidemiology, spatial statistics, sociology, etc.
Advanced Statistics with Applications in R teaches students to use theory for solving reallife problems through computations: there are about 500 R codes and 100 datasets. These data can be freely downloaded from the author's website dartmouth.edu/~eugened.
This book is suitable as a text for senior undergraduate students with major in statistics or data science or graduate students. Many researchers who apply statistics on the regular basis find explanation of many fundamental concepts from the theoretical perspective illustrated by concrete realworld applications.
Table of contents
 Cover
 WILEY SERIES IN PROBABILITY AND STATISTICS
 Why I Wrote This Book
 Chapter 1: Discrete random variables

Chapter 2: Continuous random variables
 2.1 Distribution and density functions
 2.2 Mean, variance, and other moments
 2.3 Uniform distribution
 2.4 Exponential distribution
 2.5 Moment generating function
 2.6 Gamma distribution
 2.7 Normal distribution
 2.8 Chebyshev's inequality
 2.9 The law of large numbers
 2.10 The central limit theorem
 2.11 Lognormal distribution
 2.12 Transformations and the delta method
 2.13 Random number generation
 2.14 Beta distribution
 2.15 Entropy
 2.16 Benford's law: the distribution of the first digit
 2.17 The Pearson family of distributions
 2.18 Major univariate continuous distributions

Chapter 3: Multivariate random variables
 3.1 Joint cdf and density
 3.2 Independence
 3.3 Conditional density
 3.4 Correlation and linear regression
 3.5 Bivariate normal distribution
 3.6 Joint density upon transformation
 3.7 Geometric probability
 3.8 Optimal portfolio allocation
 3.9 Distribution of order statistics
 3.10 Multidimensional random vectors
 Chapter 4: Four important distributions in statistics
 Chapter 5: Preliminary data analysis and visualization

Chapter 6: Parameter estimation
 6.1 Statistics as inverse probability
 6.2 Method of moments
 6.3 Method of quantiles
 6.4 Statistical properties of an estimator
 6.5 Linear estimation
 6.6 Estimation of variance and correlation coefficient
 6.7 Least squares for simple linear regression
 6.8 Sufficient statistics and the exponential family of distributions
 6.9 Fisher information and the Cramér–Rao bound
 6.10 Maximum likelihood
 6.11 Estimating equations and the M‐estimator

Chapter 7: Hypothesis testing and confidence intervals
 7.1 Fundamentals of statistical testing
 7.2 Simple hypothesis
 7.3 The power function of the ‐test
 7.4 The ‐test for the means
 7.5 Variance test
 7.6 Inverse‐cdf test
 7.7 Testing for correlation coefficient
 7.8 Confidence interval
 7.9 Three asymptotic tests and confidence intervals
 7.10 Limitations of classical hypothesis testing and the ‐value

Chapter 8: Linear model and its extensions
 8.1 Basic definitions and linear least squares
 8.2 The Gauss–Markov theorem
 8.3 Properties of OLS estimators under the normal assumption
 8.4 Statistical inference with linear models
 8.5 The one‐sided p‐ and d‐value for regression coefficients
 8.6 Examples and pitfalls
 8.7 Dummy variable approach and ANOVA
 8.8 Generalized linear model

Chapter 9: Nonlinear regression
 9.1 Definition and motivating examples
 9.2 Nonlinear least squares
 9.3 Gauss–Newton algorithm
 9.4 Statistical properties of the NLS estimator
 9.5 The nls function and examples
 9.6 Studying small sample properties through simulations
 9.7 Numerical complications of the nonlinear least squares
 9.8 Optimal design of experiments with nonlinear regression
 9.9 The Michaelis–Menten model
 Chapter 10: Appendix
 Bibliography
 Index
 End User License Agreement
Product information
 Title: Advanced Statistics with Applications in R
 Author(s):
 Release date: November 2019
 Publisher(s): Wiley
 ISBN: 9781118387986
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