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A Graduate Course on Statistical Inference

  • Textbook
  • © 2019

Overview

Authors:
  1. Bing Li

    1. Department of Statistics, Penn State University, University Park, USA

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    You can also search for this author in PubMed   Google Scholar

  2. G. Jogesh Babu

    1. Department of Statistics, Penn State University, University Park, USA

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    You can also search for this author in PubMed   Google Scholar

  • Adapts to a one-semester or two-semester graduate course in statistical inference
  • Employs similar conditions throughout to unify the volume and clarify theory and methodology
  • Reflects up-to-date statistical research
  • Draws upon three main themes: finite-sample theory, asymptotic theory, and Bayesian statistics

Part of the book series: Springer Texts in Statistics (STS)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XII
    Download chapter PDF

  2. Probability and Random Variables

    • Bing Li, G. Jogesh Babu
    Pages 1-29

  3. Classical Theory of Estimation

    • Bing Li, G. Jogesh Babu
    Pages 31-60

  4. Testing Hypotheses for a Single Parameter

    • Bing Li, G. Jogesh Babu
    Pages 61-98

  5. Testing Hypotheses in the Presence of Nuisance Parameters

    • Bing Li, G. Jogesh Babu
    Pages 99-134

  6. Basic Ideas of Bayesian Methods

    • Bing Li, G. Jogesh Babu
    Pages 135-172

  7. Bayesian Inference

    • Bing Li, G. Jogesh Babu
    Pages 173-201

  8. Asymptotic tools and projections

    • Bing Li, G. Jogesh Babu
    Pages 203-236

  9. Asymptotic theory for Maximum Likelihood Estimation

    • Bing Li, G. Jogesh Babu
    Pages 237-259

  10. Estimating equations

    • Bing Li, G. Jogesh Babu
    Pages 261-293

  11. Convolution Theorem and Asymptotic Efficiency

    • Bing Li, G. Jogesh Babu
    Pages 295-327

  12. Asymptotic Hypothesis Test

    • Bing Li, G. Jogesh Babu
    Pages 329-374

  13. Back Matter

    Pages 375-379
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Keywords

About this book

This textbook offers an accessible and comprehensive overview of statistical estimation and inference that reflects current trends in statistical research. It draws from three main themes throughout: the finite-sample theory, the asymptotic theory, and Bayesian statistics. The authors have included a chapter on estimating equations as a means to unify a range of useful methodologies, including generalized linear models, generalized estimation equations, quasi-likelihood estimation, and conditional inference. They also utilize a standardized set of assumptions and tools throughout, imposing regular conditions and resulting in a more coherent and cohesive volume. Written for the graduate-level audience, this text can be used in a one-semester or two-semester course.

Reviews

“This is a very nice and readable graduate level textbook of theoretical statistics. … The book is intended to be used as either a one- or a two-semester textbook of statistical inference for graduate level students, but it can also be of use to a wider group of readers interested in theoretical statistics.” (Zuzana Prášková, Mathematical Reviews, August, 2020)

Authors and Affiliations

  • Department of Statistics, Penn State University, University Park, USA

    Bing Li, G. Jogesh Babu

About the authors

Bing Li is Verne M. Wallaman Professor of Statistics at Pennsylvania State University. He is the author of Sufficient Dimension Reduction: Methods and Applications with R (2018). Dr. Li has served as an associate editor for The Annals of Statistics and is currently serving as an associate editor for Journal of the American Association.




G. Jogesh Babu is a distinguished professor of statistics, astronomy, and astrophysics, as well as director of the Center for Astrostatistics, at Pennsylvania State University. He was the 2018 winner of the Jerome Sacks Award for Cross-Disciplinary Research. He and his colleague Dr. E.D. Feigelson coined the term "astrostatistics," when they co-authored a book by the same name in 1996. Dr. Babu's numerous publications also include Statistical Challenges in Modern Astronomy V (with Feigelson, Springer 2012) and Modern Statistical Methods for Astronomy with R Applications (2012).




Bibliographic Information

  • Book Title: A Graduate Course on Statistical Inference

  • Authors: Bing Li, G. Jogesh Babu

  • Series Title: Springer Texts in Statistics

  • DOI: https://doi.org/10.1007/978-1-4939-9761-9

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2019

  • Hardcover ISBN: 978-1-4939-9759-6Published: 02 August 2019

  • eBook ISBN: 978-1-4939-9761-9Published: 02 August 2019

  • Series ISSN: 1431-875X

  • Series E-ISSN: 2197-4136

  • Edition Number: 1

  • Number of Pages: XII, 379

  • Number of Illustrations: 148 b/w illustrations

  • Topics: Statistical Theory and Methods

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