Class meetings: Monday and Wednesday 2-3:15pm in Hanes 125.
Prerequisites: Working knowledge of theoretical statistics and measure theoretic probability at the introductory graduate level. Basic real analysis and linear algebra.
Registration: Enrollment and registration for the course is handled online.
Instructor: Andrew B. Nobel, Department of Statistics and Operations Research
Office: Hanes 308 Phone: 919-962-1352.
STOR 755 is a PhD level course covering advanced
topics in statistical inference. The course is
appropriate for graduate students in Statistics,
Biostatistics and related fields of study. The
focus of the course is theoretical, emphasizing both
general results and the mathematical techniques
underlying their proof. Topics will be presented
in a detailed, mathematically rigorous fashion, and will
be as self-contained as the material allows. We
will cover asymptotic and non-asmptotic results,
with an emphasis on non-parametric problems.
Texts: There is no primary text for the course. Some of the initial material is covered in the book "Asymptotic Statistics" by Aad van der Vaart and the book. Other material will be drawn from tutorials, surveys, and research monographs.
Tentative Syllabus: The course will cover a broad range of topics, covering theoretical tools of importance and broad applicability in modern theoretical statistics. We will emphasize results whose proofs illustrate techniques of general importance. The following is a unordered, tentative list of topics. The final list will depend on available time and, to some extent, student preferences.
consistency and CLTs via the Bahadur representation
Consistency and asymptotic normality of M and Z estimators
U-statistics (one and two sample): asymptotic normality
inequalities for bounded and Gaussian random variables
comparison theorems for Gaussian random variables
Stein's method for normal
approximation. Berry-Esseen theorems
inequality and the VC dimension
Overview of some basic
results concerning chaining and empirical process
Prerequisites: Students should look over Chapter 2 of van der Vaart for a review of prerequisite material for the course. Additional material can be found in Chapter 1 of ``Mathematical Statistics'' by Jun Shao.
Reading assignments and homework
problems will be set periodically throughout the
semester. In addition, students will be asked to
read and offer written or oral comments on a paper in
the literature. More details on the project will
be provided later in the semester.
"Statistical Inference", Second Edition, by G. Casella and R.L. Berger, Duxbury, 2002.
Statistics", Second Edition, by P.J. Bickel and K.A.
Doksum, Prentice Hall, 2001.
Methods in Density Estimation", by L. Devroye and G.
Lugosi, Springer, 2001.
and Measure", Third Edition, by P. Billingsley, Wiley,
"Multivariate Analysis", by K.V. Mardia, J.T. Kent and
J.M. Bibby, Academic Press, 1979.
"The Cauchy-Schwartz Master Class'', J.M. Steele, Cambridge, 2004.
"Principles of Mathematical Analysis", Third Edition, by W. Rudin, McGraw Hill. (This book is a good reference for real analysis.)
Jon Wellner at U.W. Seattle has extensive lecture notes on theoretical statistics available on his web page.
Code: Students are expected to adhere to the UNC
honor code at all times.