### Maximum Likelihood Estimation (MLE)

Maximum Likelihood Estimation

taught by Kuber Deokar

Aim of Course:

Maximum likelihood is a popular method of estimating population parameters from a sample. It is an important component in most modeling methods, and maximum likelihood estimates are used as benchmarks against which other methods are often measured. This online course, "Maximum Likelihood Estimation" will cover the derivation of maximum likelihood estimates, and their properties. After successfully completing this course, you will understand the role that MLE plays in statistical models, and be able to assess both the advantages and disadvantages of using a maximum likelihood estimate in a particular situation. This course will provide useful conceptual foundation for those contemplating taking statistical modeling courses. (Note: The primary purpose of this course is to provide a conceptual understanding of MLE as a building block in statistical modeling. It is not to provide facility with MLE as a practical tool.)

This course may be taken individually (one-off) or as part of a certificate program.

Course Program:

## WEEK 1: Basics of Estimation, What is a ML Estimator?

- Basic definitions: sample, population, and sample mean, sample variance, population mean, population variance etc.
- Probability distributions: Standard probability distributions, derivations of expected value and variance.
- Estimation: A quick overview of basics of estimation theory (estimate, estimator etc.).
- Properties of estimators (or requisites for a good estimator): consistency, unbiasedness (also cover concept of bias and minimum bias), efficiency, sufficiency and minimum variance.
- Methods of estimation (definitions): method of moments (MOM), method of least squares (OLS) and maximum likelihood estimation (MLE).
- Why MLE is preferred? MLE vs. other methods of estimation.
- Pop quiz

## WEEK 2: Properties and Applications of ML Estimators and Bonus Readings

- MLE: properties
- MLE: derivations
- ML estimators don't always exist - examples.
- In which standard methods are ML estimators used?
- Use (or not) of ML estimators in linear regression.
- Use of ML estimators in logistic regression. Should they be used?
- Tests of hypotheses: tests based on the sampling distribution of the ML estimator
- Pop quiz
- Bonus reading material: further readings/references

HOMEWORK:

Homework in this course consists of short answer questions to test concepts and guided data analysis problems using software.

# Maximum Likelihood Estimation

Who Should Take This Course:

Maximum likelihood estimation is used in many of the methods taught in statistics.com's intermediate and advanced courses (Survival Analysis, Logistic Regression and Generalized Linear Models, to name a few). Students who need to understand the theory behind those methods should take this course first.

Level:

intermediate

Organization of the Course:

This course takes place online at the Institute for 2 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

About 15 hours per week, at times of your choosing.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
- You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's). For those successfully completing the course, CEU's and a record of course completion will be issued by The Institute, upon request.

Course Text:

Course materials will be provided by the instructor.

Software:

No specific software is required.

Access to one or more of these software packages- SAS, R, S-plus, Stata, Minitab, StatXact, LISREL, will enhance your experience with this course.

# Maximum Likelihood Estimation

April 21, 2017 to May 05, 2017November 24, 2017 to December 08, 2017April 20, 2018 to May 04, 2018November 23, 2018 to December 07, 2018