5.1 Summary

This week we will transition from probability to statistics. We will first overview the remainder of the course with an introduction to statistical inference. We will define the core principles of estimation and the inferential tasks that we will study in the coming weeks. Then we will look at our first estimator, the empirical distribution, which is a nonparametric attempt to estimate a distribution function.

5.2 Learning Objectives

After completing this week, you are expected to be able to:

• Understand the goals of statistical inference.
• Understand the definition of a statistic and an estimator.
• Calculate bias, variance, and MSE of estimators.
• Understand the relationship between parameters and distributions, and statistics and data.
• Use the empirical distribution to estimate a distribution function.
• Use the the plug-in principle to estimate statistical functionals.

5.3 Reading

5.4 Video

5.5 Assignments

• Homework 04
  • Due: Monday, March 1
  • Submission: Gradescope
  • Solution: Compass

5.6 Office Hours

5.7 Additional Information

• Wikipedia: Empirical Distribution Function