Daniel O. Scharfstein, ScD
BSPH E3547
Office Hours:  By Appointment

Teaching Assistant

Tiachen Qian
BSPH E3036
Office Hours: By Appointment

    Class Meeting Times

Tuesday/Thursday: 1:30-3:00

    Course Description

This course focuses on drawing large sample inferences about "parameters" in statistical models. We develop asymptotic    theory for maximum likelihood estimation, M-estimation, and generalized method of moment (GMM) estimation. Formal techniques for constructing estimators in semi-parametric models will be discussed. Particular attention will be paid to models for longitudinal and survival data. Guest lecturers will discuss targeted maximum likelihood, hypothesis testing, empirical likelihood. The course will involve rigorous mathematical arguments so that familiarity with concepts in advanced calculus, real analysis, and measure theory will be required.

Intended Audience

The course is designed for Biostatistics Ph.D. students in their 2nd year or beyond.  Exceptions made with permission of the instructor.


Introduction to Probability Theory I-II (550.620-1), Introduction to Statistical Theory I-II (140.673-4),  Real Analysis.

Teaching Style

Course notes will be posted on this website prior to each lecture.  The SMARTBOARD will be used in the presentation of the materials.

Method of Student Evaluation

As this is a two term sequence, one grade will be given at the end of the course which will be applied to both terms. There will be 3 problem sets each term, which will include theoretical exercises. The time allotted for each problem set will range from 10-14 days. Late assignments will not be accepted. On all problem sets, except one each term, students may give advice to one another, but work should be carried out and written up independently. No collaboration will be allowed on one designated problem set of each term. A project will be due at the end of the second term. All of the assignments will be weighted equally, except for the two independent problem sets and project which will carry twice the weight of the others.

Recommended Textbooks

  • Theory of Point Estimation, by E.L. Lehmann and G. Casella, Springer
  • A Course in Large Large Sample Theory, by T.S. Ferguson, Chapman-Hall.
  • Elements of Large-Sample Theory, by E.L. Lehmann, Springer
  • Approximation Theorems of Mathematical Statistics, by R Serfling, Wiley.
  • Asymptotic Statistics, by A.W. van der Vaart, Cambridge.
  • Large Sample Estimation and Hypothesis Testing , by W.K. Newey and D. McFadden, Handbook of Econometrics.
  • Theoretical Statistics, by D. Cox and D. Hinkley,  Chapman and Hall
  • Principles of Mathematical Analysis, by W. Rudin, McGraw Hill
  • Counting Processes and Survival Analysis, by T. Fleming and D. Harrington, Wiley
  • Probability and Measure, by P. Billingsley, Wiley
  • Real Analysis and Probability, by R. Ash, Academic Press
  • Optimization by Vector Space Methods, by D. Luenberger, Wiley
    Research Project

The purpose of the project is to (1) develop and hone the student's ability to read the literature in the area of statistical inference and theory; (2) provide experience in communicating technical material in both written and oral form; and (3) serve to prepare the student for his/her oral exams. Students will select papers from the statistical literature on a common topic involving (large sample) theory of estimation. Students should read the papers so that they are thoroughly understood (including the details of proofs). Each student will develop a 25 minute presentation, with pdf-distributable notes. The presentations will be held during the last week of the second term. Discussions with the instructor about the project are welcomed and encouraged. 

    Other Remarks

You are not allowed to look at any material from previous years, as some material on the homeworks may be recycled.  You will be asked to sign on honor statement on each independent assignment.