Mathematical Statistics

Mathematical Statistics

  • Electronic book text
By (author) 

List price: US$57.95

Currently unavailable

We can notify you when this item is back in stock

Add to wishlist

AbeBooks may have this title (opens in new window).

Try AbeBooks

Description

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.
show more

Product details

  • Electronic book text | 504 pages
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 1000 equations; 14 Tables, black and white
  • 1584888563
  • 9781584888567

Table of contents

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 Cramer-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
show more