Syllabus

Course Meeting Times

Lectures: 1.5 hrs / session; 2 sessions / week

Recitations: 1.5 hrs / session; 1 session / week

Prerequisites

18.02 Multivariable Calculus

Course Description

This course is divided into two sections, Part I and Part II. Part I, found here, provides an introduction to statistical theory. A brief review of probability will be given mainly as background material, however, it is assumed to be known. Topics include normal distribution, limit theorems, Bayesian concepts, and testing, among others.

Textbooks

Buy at Amazon Casella, George and Roger Berger. Statistical Inference. 2nd Edition. Cengage Learning, 2001. ISBN: 9780534243128.

This book covers all of the material of the course and, in addition, provides many problems for practice as well as excellent references.

Course Outline

Numbers after each section refer to sections of the text.

  1. Samples and Their Characteristics: Sample vs. Population, Histogram, Sample Moments, Order Statistics (5.1–5.4)
  2. Types of Convergence and Limit Theorems: LLN, CLT, Slutsky Theorem, Chebyshev’s Inequality (5.5)
  3. Summarizing Data: Sufficient Statistics, Minimal Sufficient Statistic, Ancillary Statistics (6.1–6.4)
  4. Point Estimates and Their Comparison: Unbiasness, MSE, Rao-Cramer Bound, Information Matrix; Asymptotic Behavior: Consistency, Asymptotic Normality, Asymptotic Efficiency (7.3)
  5. Method of Moments (7.2.1)
  6. Maximum Likelihood (7.2.2)
  7. Testing: Size and Power, UMP Test and Neyman-Pearson Lemma, Wald Test (8.1–8.3)
  8. Confidence Sets Construction (9.1–9.3)

Grading

Activity Percentage
Midterm 35%
Problem Sets 15%

Part I consists of 50% of the course. The other 50% is determined in Part II. 

There will be a midterm worth 35%. There will be 6 problem sets. A solution to one problem (marked) from each problem set should be handed in to the Teaching Assistant (TA) at the beginning of the lecture or sent to the TA via e-mail before the lecture. This will constitute 15% of the grade. The solution to this problem will be posted after the due date. No late assignments will be accepted. All other problems are for your own study; the solutions to them won’t be posted, but will be discussed during the recitations. One problem from the problem sets will appear on the mid-term exam.