Mathematical Statistics: 1st Edition (Hardback) book cover

Mathematical Statistics

1st Edition

By Keith Knight

Chapman and Hall/CRC

504 pages

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Hardback: 9781584881780
pub: 1999-11-24
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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.

Features

  • Provides the tools that allow an understanding of the underpinnings of statistical methods
  • Encourages the use of statistical software, which widens the range of problems reader can consider
  • Brings relevance to the subject-shows readers it has much to offer beyond optimality theory
  • Focuses on inferential procedures within the framework of parametric models, but also views estimation from the nonparametric perspective
  • Solutions manual availalbe on crcpress.com
  • Reviews

    Keith Knight's new book is a welcome addition to textbooks appropriate for masters-level theory courses. … His is the best treatment of likelihood theory that I know at any level. … I wish I had a nickel for every time I have been asked for recommended reading on likelihood theory and had to say one did not exist at this level. Now I can wholeheartedly recommend Mathematical Statistics.

    C. GEYER, University of Minnesota in Journal of the American Statistical Association, June 2001

    "…a very suitable text for teaching at an acceptable mathematical level…contains numerous examples and each chapter is followed by a rich choice of exercises…this makes the book excellent for teaching,"

    -Short Book Reviews of the ISI

    "well-written,,,far greater coverage of ides that are not standard in other mathematical statistics texts."

    --M. S. Ridout, Institute of Mathematics and Statistics, University of Kent at Canterbury, UK in Biometrics

    "…one of the five best textbooks on a beginning course on theoretical statistics providing a good grasp on the foundations of theoretical statistics. Primarily for graduate students with mathematical backgrounds in linear algebra, multivariable calculus, and some exposure to statistical methodology. Highly recommended for all academic libraries."

    --D. V. Chopra, Wichita State University in CHOICE

    "This books breaks away form more theoretically burdensome texts, focusing on providing a set of useful tools that help readers understand the theoretical under pinning of statistical methodology."

    --SciTech Book News, March 2000

    "This (hardback) book is one of the most up-to-date and easily understood texts in the field of mathematical statistics. The author has recognized the difficult nature of the subject and has done justice to the subject by finally producing one of the best well-rounded texts for graduate and senior undergraduate students. …well written and well structured. This text would be a very useful teaching tool.""

    The Statistician, Vol. 50, Part 2, 2001

    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 Cramér-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

    About the Series

    Chapman & Hall/CRC Texts in Statistical Science

    Learn more…

    Subject Categories

    BISAC Subject Codes/Headings:
    MAT029000
    MATHEMATICS / Probability & Statistics / General
    MAT029010
    MATHEMATICS / Probability & Statistics / Bayesian Analysis