Constantine Frangakis
Department of Biostatistics
Bloomberg School of Public Health
Johns Hopkins University
cfrangak@jhsph.edu

Advanced Statistical Theory I-II
(140.771-2, 2007)

Meeting times: Tuesdays, Thursdays 1:30-3:00 pm, W2009
Instructor: Constantine E. Frangakis, Associate Professor, Biostatistics, Hygiene E3642
   cfrangak@jhsph.edu
TA:  Sheng Luo, sluo@jhsph.edu
Office hour: Thursday 3-4pm, W3038

Course description

The course examines statistics as a discipline along the path towards making decisions. First, the course examines the justification of statistics from axioms on informed preferences and its close connection to Bayesian theory. Then, the course examines the role of standardizing intermediate steps, through various additional restrictions on estimation, and studies the properties of the resulting methods.

The instructor acknowledges the partial sharing of notes by H Chernoff, DB Rubin, and DO Scharfstein.

Syllabus

Summaries of the lectures will be posted after each class

Lecture notes

Section 1                              Large sample theory of MLE: (1.1) (1.2) (1.3) (1.4) (1.5)

Section 2                              Partial likelihood

Section 3                              Large sample theory of M- and generalized moment estimation

Section 4                              Problems with many nuisance parameters
                                              part 1: Semiparametric theory

Section 5                              Problems with many nuisance parameters
                                              part 2: Empirical Bayes

Section 6                              U-statistics                                           

Section 7                              Markov chains

Section 8                              Introduction to martingales and survival analysis

Problem sets

Problem set 1 (Solution)

Problem set 2 data set (Solution)

Problem set 3