Course in Mathematical Statistics and Large Sample Theory

Rabi Bhattacharya, PhD, has held regular faculty positions at UC, Berkeley; Indiana University; and the University of Arizona.  He is a Fellow of the Institute of Mathematical Statistics and a recipient of the U.S. Senior Scientist Humboldt Award and of a Guggenheim Fellowship.  He has served on editorial boards of many international journals and has published several research monographs and graduate texts on probability and statistics, including Nonparametric Inference on Manifolds, co-authored with A. Bhattacharya.Lizhen Lin, PhD, is Assistant Professor in the Department of Statistics and Data Science at the University of Texas at Austin.  She received a PhD in Mathematics from the University of Arizona and was a Postdoctoral Associate at Duke University.  Bayesian nonparametrics, shape constrained inference, and nonparametric inference on manifolds are among her areas of expertise. Vic Patrangenaru, PhD, is Professor of Statistics at Florida State University.  He received PhDs in Mathematics from Haifa, Israel, and from Indiana University in the fields of differential geometry and statistics, respectively.  He has many research publications on Riemannian geometry and especially on statistics on manifolds.  He is a co-author with L. Ellingson of Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis.

"It deals with advanced statistical theory with a special focus on statistical inference and large sample theory, aiming to cover the material for a modern two-semester graduate course in mathematical statistics. ... Overall, the book is very advanced and is recommended to graduate students with sound statistical backgrounds, as well as to teachers, researchers, and practitioners who wish to acquire more knowledge on mathematical statistics and large sample theory." (Lefteris Angelis, Computing Reviews, March, 2017) "This is a very nice book suitable for a theoretical statistics course after having worked through something at the level of Casella & Berger, as well as some measure theory. ... In addition to the exercises, which range from doable to interesting, there are several projects scattered throughout the text. The explanations are clear and crisp, and the presentation is interesting. ... the book would be a worthy addition to your statistics library." (Peter Rabinovitch, MAA Reviews, maa.org, March, 2017)

• 1 Introduction.- 2 Decision Theory.- 3 Introduction to General Methods of Estimation.- 4 Sufficient Statistics, Exponential Families, and Estimation.- 5 Testing Hypotheses.- 6 Consistency and Asymptotic Distributions and Statistics.- 7 Large Sample Theory of Estimation in Parametric Models.- 8 Tests in Parametric and Nonparametric Models.- 9 The Nonparametric Bootstrap.- 10 Nonparametric Curve Estimation.- 11 Edgeworth Expansions and the Bootstrap.- 12 Frechet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces.- 13 Multiple Testing and the False Discovery Rate.- 14 Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory.- 15 Miscellaneous Topics.- Appendices.- Solutions of Selected Exercises in Part 1.