A Graduate Course on Statistical Inference

1. Front Matter

   Pages I-XII

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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

    PDF

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.

• Bayes
• Bayesian
• Cauchy-Schwarz
• statistical inference
• statistical estimation
• finite-sample estimation
• differentiable under the integral sign
• stochastic equicontinuity
• finite-sample theory
• asymptotic theory
• posterior distributions
• empirical Bayes
• shrinkage estimates
• Le Cam-Hajek
• estimating equations
• generalized linear models
• quasi-likelihood estimation
• conditional inference
• Local Asymptotic Normal

“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)

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

  Bing Li, G. Jogesh Babu

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).

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