A Course in Mathematical Statistics and Large Sample Theory

ISBN-13: 9781493940301 / Angielski / Twarda / 2016 / 389 str.

Rabi Bhattacharya; Lizhen Lin; Victor Patrangenaru

Opis

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics.
Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

Recenzje

"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)

Spis treści

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.

O autorze

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. 

Blurb

This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics.

Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics — parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

• Large Sample theory with many worked examples, numerical calculations, and simulations to illustrate theory
  
• Appendices provide ready access to a number of standard results, with many proofs
  
• Solutions given to a number of selected exercises from Part I
  
• Part II exercises with a certain level of difficulty appear with detailed hints
  

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.