Statistics 610 (Fall 2013)

Statistical Inference

Revised: 28 Aug 2013

A systematic development of the mathematical theory of statistical inference covering methods of estimation, hypothesis testing, and confidence intervals. An introduction to statistical decision theory. Undergraduate probability at the level of Statistics 241a assumed.

Instructor: David Pollard
When: Tues, Thurs 10:30am - 11:45am
Where: 24 Hillhouse, Rm 107
Office hours: 4:00-5:30 Tues, Wed
TA: Chao Gao
Problem session: to be arranged if needed
Intended audience: Students (both graduate and undergraduate) who are comfortable with introductory probability (as covered in Stat 241/541).
Text: No single text. I find last year's text,
Young and Smith (2010) Essentials of Statistical Inference, Cambridge University Press,
a useful overview but I do not intend to cover the material in the same way or even in the same order. Instead I will draw from multiple sources, many of which are available for free.
Topics (tentative): Ideas to be explained, not necessarily in the following order:
  • Statistical models
    • sampling models
    • models as an aid to thinking
    • randomization
  • Estimation and "margins of error"
    • maximum likelihood and M-estimators
    • asymptotic theory
    • information inequality
    • efficiency
    • sufficiency
    • confidence intervals
    • robustness
    • unbiasedness (Is it important?)
  • Likelihood theory
    • philosophy
    • score function
    • likelihood ratio tests
  • Bayes theory
    • independence vs. exchangeability
  • Decision theory and related ideas
    • hypothesis testing
    • goodness of fit
    • loss functions; risk; admissibility
    • false discovery control
    • Stein shrinkage
    • sparsity
  • Computation vs. theory
    • bootstrap
Grades: No exams.
  • The final grade will be based completely on the weekly homework.
  • Homework due each Thursday. All help received for the homework must be explicitly acknowledged.
  • Students who wish to work in teams (no more than 2 to a team) should submit a single a solution set. All members of a team will be expected to understand the team's solutions sufficiently well to explain the reasoning at the blackboard. Occasional meetings with DP will be arranged.
Other: Miscellaneous helpful materials.
  • Handouts.
  • Class materials for an introductory probability course (Stat 241/541, Fall 2005), containing more extensive elementary discussion of probabilistic ideas. See, in particular, the first two chapters, on (conditional) probability and (conditional) expectations.