Asymptotic Theory of Statistics and Probability

Asymptotic Theory of Statistics and Probability by Anirban DasGupta.

This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the im...

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Bibliographic Details
Main Author: DasGupta, Anirban (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 2008.
Edition:1st ed. 2008.
Series:Springer Texts in Statistics,
Springer eBook Collection.
Subjects:
Probabilities.
Statistics .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Basic Convergence Concepts and Theorems
  • Metrics, Information Theory, Convergence, and Poisson Approximations
  • More General Weak and Strong Laws and the Delta Theorem
  • Transformations
  • More General Central Limit Theorems
  • Moment Convergence and Uniform Integrability
  • Sample Percentiles and Order Statistics
  • Sample Extremes
  • Central Limit Theorems for Dependent Sequences
  • Central Limit Theorem for Markov Chains
  • Accuracy of Central Limit Theorems
  • Invariance Principles
  • Edgeworth Expansions and Cumulants
  • Saddlepoint Approximations
  • U-statistics
  • Maximum Likelihood Estimates
  • M Estimates
  • The Trimmed Mean
  • Multivariate Location Parameter and Multivariate Medians
  • Bayes Procedures and Posterior Distributions
  • Testing Problems
  • Asymptotic Efficiency in Testing
  • Some General Large-Deviation Results
  • Classical Nonparametrics
  • Two-Sample Problems
  • Goodness of Fit
  • Chi-square Tests for Goodness of Fit
  • Goodness of Fit with Estimated Parameters
  • The Bootstrap
  • Jackknife
  • Permutation Tests
  • Density Estimation
  • Mixture Models and Nonparametric Deconvolution
  • High-Dimensional Inference and False Discovery
  • A Collection of Inequalities in Probability, Linear Algebra, and Analysis.

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