# 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:
`R`

Markdown - 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! |