The Empirical Distribution
Week 05, Spring 2022
- Start: Monday, February 14
- End: Friday, February 18
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.
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.
Reading
| Source | Section |
|---|---|
| Wasserman | 6.1 - 6.3 |
| Wasserman | 7.1 - 7.2 |
| Evans and Rosenthal | 5.1 - 5.5 |
| Marden | 10.1 - 10.4 |
| Marden | 11.1 - 11.5 |
Video
| Title and Slides | Link | Mirror |
|---|---|---|
| 5.0 - Welcome to Week 05 | 5.0 - YouTube | 5.0 - ClassTranscribe |
| 5.1 - Statistical Inference | 5.1 - YouTube | 5.1 - ClassTranscribe |
| 5.2 - The Empirical Distribution | 5.2 - YouTube | 5.2 - ClassTranscribe |
Assignments
- Homework 04
- Source:
RMarkdown - Due: Monday, February 21
- Submission: Gradescope
- Solution: Canvas
- Source:
Office Hours
| Staff and Link | Day | Time |
|---|---|---|
| Zoom with David | Monday | 3:00 PM - 4:00 PM |
| Zoom with Eugene | Monday | 9:00 PM - 10:00 PM |
| Zoom with Eugene | Thursday | 12:00 PM - 1:00 PM |
| Zoom with David | Thursday | 5:00 PM - 7:00 PM |
| Discussion Forum | Any! | Any! |