Mathematical Statistics and Data Analysis

ISBN-10: 0534399428

ISBN-13: 9780534399429

Edition: 3rd 2007

Authors: John A. Rice

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Description:

This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings.
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Book details

List price: $319.95
Edition: 3rd
Copyright year: 2007
Publisher: Brooks/Cole
Publication date: 4/28/2006
Binding: Hardcover
Pages: 688
Size: 7.25" wide x 9.25" long x 1.25" tall
Weight: 2.970
Language: English

Preface
Probability
Introduction
Sample Spaces
Probability Measures
Computing Probabilities: Counting Methods
The Multiplication Principle
Permutations and Combinations
Conditional Probability
Independence
Concluding Remarks
Problems
Random Variables
Discrete Random Variables
Bernoulli Random Variables
The Binomial Distribution
The Geometric and Negative Binomial Distributions
The Hypergeometric Distribution
The Poisson Distribution
Continuous Random Variables
The Exponential Density
The Gamma Density
The Normal Distribution
The Beta Density
Functions of a Random Variable
Concluding Remarks
Problems
Joint Distributions
Introduction
Discrete Random Variables
Continuous Random Variables
Independent Random Variables
Conditional Distributions
The Discrete Case
The Continuous Case
Functions of Jointly Distributed Random Variables
Sums and Quotients
The General Case
Extrema and Order Statistics
Problems
Expected Values
The Expected Value of a Random Variable
Expectations of Functions of Random Variables
Expectations of Linear Combinations of Random Variables
Variance and Standard Deviation
A Model for Measurement Error
Covariance and Correlation
Conditional Expectation and Prediction
Definitions and Examples
Prediction
The Moment-Generating Function
Approximate Methods
Problems
Limit Theorems
Introduction
The Law of Large Numbers
Convergence in Distribution and the Central Limit Theorem
Problems
Distributions Derived from the Normal Distribution
Introduction
x[superscript 2], t, and F Distributions
The Sample Mean and the Sample Variance
Problems
Survey Sampling
Introduction
Population Parameters
Simple Random Sampling
The Expectation and Variance of the Sample Mean
Estimation of the Population Variance
The Normal Approximation to the Sampling Distribution of X
Estimation of a Ratio
Stratified Random Sampling
Introduction and Notation
Properties of Stratified Estimates
Methods of Allocation
Concluding Remarks
Problems
Estimation of Parameters and Fitting of Probability Distributions
Introduction
Fitting the Poisson Distribution to Emissions of Alpha Particles
Parameter Estimation
The Method of Moments
The Method of Maximum Likelihood
Maximum Likelihood Estimates of Multinomial Cell Probabilities
Large Sample Theory for Maximum Likelihood Estimates
Confidence Intervals from Maximum Likelihood Estimates
The Bayesian Approach to Parameter Estimation
Further Remarks on Priors
Large Sample Normal Approximation to the Posterior
Computational Aspects
Efficiency and the Cramer-Rao Lower Bound
An Example: The Negative Binomial Distribution
Sufficiency
A Factorization Theorem
The Rao-Blackwell Theorem
Concluding Remarks
Problems
Testing Hypotheses and Assessing Goodness of Fit
Introduction
The Neyman-Pearson Paradigm
Specification of the Significance Level and the Concept of a p-value
The Null Hypothesis
Uniformly Most Powerful Tests
The Duality of Confidence Intervals and Hypothesis Tests
Generalized Likelihood Ratio Tests
Likelihood Ratio Tests for the Multinomial Distribution
The Poisson Dispersion Test
Hanging Rootograms
Probability Plots
Tests for Normality
Concluding Remarks
Problems
Summarizing Data
Introduction
Methods Based on the Cumulative Distribution Function
The Empirical Cumulative Distribution Function
The Survival Function
Quantile-Quantile Plots
Histograms, Density Curves, and Stem-and-Leaf Plots
Measures of Location
The Arithmetic Mean
The Median
The Trimmed Mean
M Estimates
Comparison of Location Estimates
Estimating Variability of Location Estimates by the Bootstrap
Measures of Dispersion
Boxplots
Exploring Relationships with Scatterplots
Concluding Remarks
Problems
Comparing Two Samples
Introduction
Comparing Two Independent Samples
Methods Based on the Normal Distribution
Power
A Nonparametric Method-The Mann-Whitney Test
Bayesian Approach
Comparing Paired Samples
Methods Based on the Normal Distribution
A Nonparametric Method-The Signed Rank Test
An Example-Measuring Mercury Levels in Fish
Experimental Design
Mammary Artery Ligation
The Placebo Effect
The Lanarkshire Milk Experiment
The Portacaval Shunt
FD&C Red No. 40
Further Remarks on Randomization
Observational Studies, Confounding, and Bias in Graduate Admissions
Fishing Expeditions
Concluding Remarks
Problems
The Analysis of Variance
Introduction
The One-Way Layout
Normal Theory; the F Test
The Problem of Multiple Comparisons
A Nonparametric Method-The Kruskal-Wallis Test
The Two-Way Layout
Additive Parametrization
Normal Theory for the Two-Way Layout
Randomized Block Designs
A Nonparametric Method-Friedman's Test
Concluding Remarks
Problems
The Analysis of Categorical Data
Introduction
Fisher's Exact Test
The Chi-Square Test of Homogeneity
The Chi-Square Test of Independence
Matched-Pairs Designs
Odds Ratios
Concluding Remarks
Problems
Linear Least Squares
Introduction
Simple Linear Regression
Statistical Properties of the Estimated Slope and Intercept
Assessing the Fit
Correlation and Regression
The Matrix Approach to Linear Least Squares
Statistical Properties of Least Squares Estimates
Vector-Valued Random Variables
Mean and Covariance of Least Squares Estimates
Estimation of [gamma superscript 2]
Residuals and Standardized Residuals
Inference about [beta]
Multiple Linear Regression-An Example
Conditional Inference, Unconditional Inference, and the Bootstrap
Local Linear Smoothing
Concluding Remarks
Problems
Common Distributions
Tables
Bibliography
Answers to Selected Problems
Author Index
Applications Index
Subject Index
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