Course Information for STOR 755, Fall 2014
 
Estimation and Hypothesis Testing (Still under Construction)


 

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.

Office Hours: TBA
 

Course Overview: 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.

    The Glivenko-Cantelli theorem

    The multivariate delta method

    Sample percentiles: consistency and CLTs via the Bahadur representation

    Consistency and asymptotic normality of M and Z estimators  

    U-statistics (one and two sample): asymptotic normality    

    Basic concentration inequalities for bounded and Gaussian random variables

    Interpolation and comparison theorems for Gaussian random variables

    Stein's method for normal approximation.  Berry-Esseen theorems

    The Vapnik-Chervonenkis inequality and the VC dimension

    Overview of some basic results concerning chaining and empirical process theory 

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. 

Grading: 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.


Other sources:

"Statistical Inference", Second Edition, by G. Casella and R.L. Berger, Duxbury, 2002.

"Mathematical Statistics", Second Edition, by P.J. Bickel and K.A. Doksum, Prentice Hall, 2001.

"Combinatorial Methods in Density Estimation", by L. Devroye and G. Lugosi, Springer, 2001.

"Probability and Measure", Third Edition, by P. Billingsley, Wiley, 1995.

"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.
 

Honor Code: Students are expected to adhere to the UNC honor code at all times.