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Chapter 1
Introduction
1.1 What Is Computational Statistics?
1.2 An Overview of the Book
Philosophy
What Is Covered
A Word About Notation
1.3 MATLAB Code
Computational Statistics Toolbox
Internet Resources
1.4 Further Reading
Chapter 2
Probability Concepts
2.1 Introduction
2.2 Probability
Background
Probability
Axioms of Probability
2.3 Conditional Probability and Independence
Conditional Probability
Independence
Bayes Theorem
2.4 Expectation
Mean and Variance
Skewness
Kurtosis
2.5 Common Distributions
Binomial
Poisson
Uniform
Normal
Exponential
Gamma
Chi-Square
Weibull
Beta
© 2002 by Chapman & Hall/CRC
viii Computational Statistics Handbook with MATLAB
Multivariate Normal
2.6 MATLAB Code
2.7 Further Reading
Exercises
Chapter 3
Sampling Concepts
3.1 Introduction
3.2 Sampling Terminology and Concepts
Sample Mean and Sample Variance
Sample Moments
Covariance
3.3 Sampling Distributions
3.4 Parameter Estimation
Bias
Mean Squared Error
Relative Efficiency
Standard Error
Maximum Likelihood Estimation
Method of Moments
3.5 Empirical Distribution Function
Quantiles
3.6 MATLAB Code
3.7 Further Reading
Exercises
Chapter 4
Generating Random Variables
4.1 Introduction
4.2 General Techniques for Generating Random Variables
Uniform Random Numbers
Inverse Transform Method
Acceptance-Rejection Method
4.3 Generating Continuous Random Variables
Normal Distribution
Exponential Distribution
Gamma
Chi-Square
Beta
Multivariate Normal
Generating Variates on a Sphere
4.4 Generating Discrete Random Variables
Binomial
Poisson
Discrete Uniform
© 2002 by Chapman & Hall/CRC
Table of Contents ix
4.5 MATLAB Code
4.6 Further Reading
Exercises
Chapter 5
Exploratory Data Analysis
5.1 Introduction
5.2 Exploring Univariate Data
Histograms
Stem-and-Leaf
Quantile-Based Plots - Continuous Distributions
Q-Q Plot
Quantile Plots
Quantile Plots - Discrete Distributions
Poissonness Plot
Binomialness Plot
Box Plots
5.3 Exploring Bivariate and Trivariate Data
Scatterplots
Surface Plots
Contour Plots
Bivariate Histogram
3-D Scatterplot
5.4 Exploring Multi-Dimensional Data
Scatterplot Matrix
Slices and Isosurfaces
Star Plots
Andrews Curves
Parallel Coordinates
Projection Pursuit
Projection Pursuit Index
Finding the Structure
Structure Removal
Grand Tour
5.5 MATLAB Code
5.6 Further Reading
Exercises
Chapter 6
Monte Carlo Methods for Inferential Statistics
6.1 Introduction
6.2 Classical Inferential Statistics
Hypothesis Testing
Confidence Intervals
6.3 Monte Carlo Methods for Inferential Statistics
© 2002 by Chapman & Hall/CRC
x Computational Statistics Handbook with MATLAB
Basic Monte Carlo Procedure
Monte Carlo Hypothesis Testing
Monte Carlo Assessment of Hypothesis Testing
6.4 Bootstrap Methods
General Bootstrap Methodology
Bootstrap Estimate of Standard Error
Bootstrap Estimate of Bias
Bootstrap Confidence Intervals
Bootstrap Standard Confidence Interval
Bootstrap-t Confidence Interval
Bootstrap Percentile Interval
6.5 MATLAB Code
6.6 Further Reading
Exercises
Chapter 7
Data Partitioning
7.1 Introduction
7.2 Cross-Validation
7.3 Jackknife
7.4 Better Bootstrap Confidence Intervals
7.5 Jackknife-After-Bootstrap
7.6 MATLAB Code
7.7 Further Reading
Exercises
Chapter 8
Probability Density Estimation
8.1 Introduction
8.2 Histograms
1-D Histograms
Multivariate Histograms
Frequency Polygons
Averaged Shifted Histograms
8.3 Kernel Density Estimation
Univariate Kernel Estimators
Multivariate Kernel Estimators
8.4 Finite Mixtures
Univariate Finite Mixtures
Visualizing Finite Mixtures
Multivariate Finite Mixtures
EM Algorithm for Estimating the Parameters
Adaptive Mixtures
8.5 Generating Random Variables
8.6 MATLAB Code
© 2002