Mathematical Statistics with Resampling and R

ISBN-10: 1118029852
ISBN-13: 9781118029855
Edition: 2011
List price: $181.00 Buy it from $90.83
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Description: This groundbreaking book shows how apply modern resampling techniques to mathematical statistics. The book includes permutation tests and bootstrap methods and classical inference methods. Resampling helps students understand the meaning of sampling  More...

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Book details

List price: $181.00
Copyright year: 2011
Publisher: John Wiley & Sons Canada, Limited
Publication date: 9/6/2011
Binding: Hardcover
Pages: 432
Size: 6.25" wide x 9.50" long x 1.00" tall
Weight: 1.870
Language: English

This groundbreaking book shows how apply modern resampling techniques to mathematical statistics. The book includes permutation tests and bootstrap methods and classical inference methods. Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. The use of R throughout the book underscores the significance of resampling since its implementation is fast enough to be both convenient and explanatory. While computer clock speeds have leveled off, new multi-core computers are well suited for parallel applications like resampling. The book contains examples, figures, exercise sets, case studies, and helpful remarks. An author-maintained web site is available.

Preface
Data and Case Studies
Case Study: Flight Delays
Case Study: Birth Weights of Babies
Case Study: Verizon Repair Times
Sampling
Parameters and Statistics
Case Study: General Social Survey
Sample Surveys
Case Study: Beer and Hot Wings
Case Study: Black Spruce Seedlings
Studies
Exercises
Exploratory Data Analysis
Basic Plots
Numeric Summaries
Center
Spread
Shape
Boxplots
Quantiles and Normal Quantile Plots
Empirical Cumulative Distribution Functions
Scatter Plots
Skewness and Kurtosis
Exercises
Hypothesis Testing
Introduction to Hypothesis Testing
Hypotheses
Permutation Tests
Implementation Issues
One-Sided and Two-Sided Tests
Other Statistics
Assumptions
Contingency Tables
Permutation Test for Independence
Chi-Square Reference Distribution
Chi-Square Test of Independence
Test of Homogeneity
Goodness-of-Fit: All Parameters Known
Goodness-of-Fit: Some Parameters Estimated
Exercises
Sampling Distributions
Sampling Distributions
Calculating Sampling Distributions
The Central Limit Theorem
CLT for Binomial Data
Continuity Correction for Discrete Random Variables
Accuracy of the Central Limit Theorem
CLT for Sampling Without Replacement
Exercises
The Bootstrap
Introduction to the Bootstrap
The Plug-In Principle
Estimating the Population Distribution
How Useful Is the Bootstrap Distribution?
Bootstrap Percentile Intervals
Two Sample Bootstrap
The Two Independent Populations Assumption
Other Statistics
Bias
Monte Carlo Sampling: The "Second Bootstrap Principle"
Accuracy of Bootstrap Distributions
Samnle Mean: Large Sample Size
Sample Mean: Small Sample Size
Sample Median
How Many Bootstrap Samples are Needed?
Exercises
Estimation
Maximum Likelihood Estimation
Maximum Likelihood for Discrete Distributions
Maximum Likelihood for Continuous Distributions
Maximum Likelihood for Multiple Parameters
Method of Moments
Properties of Estimators
Unbiasedness
Efficiency
Mean Square Error
Consistency
Transformation Invariance
Exercises
Classical Inference: Confidence Intervals
Confidence Intervals for Means
Confidence Intervals for a Mean, $$$ Known
Confidence Intervals for a Mean, $$$ Unknown
Confidence Intervals for a Difference in Means
Confidence Intervals in General
Location and Scale Parameters
One-Sided Confidence Intervals
Confidence Intervals for Proportions
The Agresti-Coull Interval for a Proportion
Confidence Interval for the Difference of Proportions
Bootstrap t Confidence Intervals
Comparing Bootstrap t and Formula t Confidence Intervals
Exercises
Classical Inference: Hypothesis Testing
Hypothesis Tests for Means and Proportions
One Population
Comparing Two Populations
Type I and Type II Errors
Type I Errors
Type II Errors and Power
More on Testing
On Significance
Adjustments for Multiple Testing
P-values Versus Critical Regions
Likelihood Ratio Tests
Simple Hypotheses and the Neyman-Pearson Lemma
Generalized Likelihood Ratio Tests
Exercises
Regression
Covariance
Correlation
Least-Squares Regression
Regression Toward the Mean
Variation
Diagnostics
Multiple Regression
The Simple Linear Model
Inference for � and �
Inference for the Response
Comments About Assumptions for the Linear Model
Resampling Correlation and Regression
Permutation Tests
Bootstrap Case Study: Bushmeat
Logistic Regression
Inference for Logistic Regression
Exercises
Bayesian Methods
Bayes' Theorem
Binomial Data, Discrete Prior Distributions
Binomial Data, Continuous Prior Distributions
Continuous Data
Sequential Data
Exercises
Additional Topics
Smoothed Bootstrap
Kernel Density Estimate
Parametric Bootstrap
The Delta Method
Stratified Sampling
Computational Issues in Bayesian Analysis
Monte Carlo Integration
Importance Sampling
Ratio Estimate for Importance Sampling
Importance Sampling in Bayesian Applications
Exercises
Review of Probability
Basic Probability
Mean and Variance
The Mean of a Sample of Random Variables
The Law of Averages
The Normal Distribution
Sums of Normal Random Variables
Higher Moments and the Moment Generating Function
Probability Distributions
The Bernoulli and Binomial Distributions
The Multinomial Distribution
The Geometric Distribution
The Negative Binomial Distribution
The Hypergeometric Distribution
The Poisson Distribution
The Uniform Distribution
The Exponential Distribution
The Gamma Distribution
The Chi-Square Distribution
The Student's t Distribution
The Beta Distribution
The F Distribution
Exercises
Distributions Quick Reference
Solutions to Odd-Numbered Exercises
Bibliography
Index

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