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Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section

**Features**

INTRODUCTION TO PROBABILITY

Random Experiments

Probability Measures

Conditional Probability and Independence

Random Variables

Expected Values

RANDOM VECTORS AND JOINT DISTRIBUTIONS

Introduction

Discrete and Continuous Random Vectors

Conditional Distributions

Normal Distributions

Poisson Processes

Generating Random Variables

CONVERGENCE OF RANDOM VARIABLES

Introduction

Convergence in Probability and Distribution

WLLN

Proving Convergence in Distribution

CLT

Some Applications

Convergence with Probability 1

PRINCIPLES OF POINT ESTIMATION

Introduction

Statistical Models

Sufficiency

Point Estimation

Substitution Principle

Influence Curves

Standard Errors

Relative Efficiency

The Jackknife

LIKELIHOOD-BASED ESTIMATION

Introduction

The Likelihood Function

The Likelihood Principle

Asymptotics for MLEs

Misspecified Models

Nonparametric Maximum Likelihood Estimation

Numerical Computation

Bayesian Estimation

OPTIMAL ESTIMATION

Decision Theory

UMVUEs

The CramÃ©r-Rao Lower Bound

Asymptotic Efficiency

INTERVAL ESTIMATION AND HYPOTHESIS TESTING

Confidence Intervals and Regions

Highest Posterior Density Regions

Hypothesis Testing

Likelihood Ratio Tests

Other Issues

LINEAR AND GENERALIZED LINEAR MODELS

Linear Models

Estimation

Testing

Non-Normal Errors

Generalized Linear Models

Quasi-Likelihood Models

GOODNESS OF FIT

Introduction

Tests Based on the Multinomial Distribution

Smooth Goodness of Fit Tests

REFERENCES

Each chapter also contains a Problems and Complements section