Statistical Theory

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A01=Felix Abramovich
A01=Ya'acov Ritov
advanced undergraduate statistics
Affine Estimators
asymptotic analysis
Author_Felix Abramovich
Author_Ya'acov Ritov
Bayes Action
Bayes Risk
Bayes Rule
Bayesian inference
Bernoulli Trials
Category=PBT
Confidence Interval
confidence intervals
Confidence Region
Conjugate Prior
Credible Set
elements of decision theory
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exponential Family
Fisher Information Matrix
fundamental concepts of statistical theory
HPD Interval
hypothesis testing
Jeffreys Prior
linear models and linear regression
mathematical statistics
Minimal Sufficient Statistic
Minimax Estimator
Minimax Risk
Minimax Rule
MLE Estimate
MP Test
nonparametric analysis
parameter estimation
Point Null Hypothesis
Posterior Distribution
Posterior Odds
principles of major statistical concepts
probability distributions
quantitative research techniques
Rao Blackwell Theorem
statistical inference methods
statistical theory for graduate students
UMVUE
Unbiased Estimator

Product details

  • ISBN 9781032007458
  • Weight: 600g
  • Dimensions: 178 x 254mm
  • Publication Date: 23 Dec 2022
  • Publisher: Taylor & Francis Ltd
  • Publication City/Country: GB
  • Product Form: Hardback
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Designed for a one-semester advanced undergraduate or graduate statistical theory course, Statistical Theory: A Concise Introduction, Second Edition clearly explains the underlying ideas, mathematics, and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, linear models, nonparametric statistics, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs.

Based on the authors’ lecture notes, the book is self-contained, which maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments.

Features:

  • Second edition has been updated with a new chapter on Nonparametric Estimation; a significant update to the chapter on Statistical Decision Theory; and other updates throughout
  • No requirement for heavy calculus, and simple questions throughout the text help students check their understanding of the material
  • Each chapter also includes a set of exercises that range in level of difficulty
  • Self-contained, and can be used by the students to understand the theory
  • Chapters and sections marked by asterisks contain more advanced topics and may be omitted
  • Special chapters on linear models and nonparametric statistics show how the main theoretical concepts can be applied to well-known and frequently used statistical tools

The primary audience for the book is students who want to understand the theoretical basis of mathematical statistics—either advanced undergraduate or graduate students. It will also be an excellent reference for researchers from statistics and other quantitative disciplines.

Felix Abramovich is a professor at the Department of Statistics and Operations Research at Tel Aviv University.

Ya’acov Ritov is a professor in the Department of Statistics at the University of Michigan, Ann Arbor. He is a professor emeritus of Statistics at the Hebrew University of Jerusalem.

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