Chapter 2 M2: Parameter estimation: theory and methods

In this module we start thinking about parameters and how to get guesses about their value (estimates) using estimators. It turns out there are multiple ways to create estimators, depending on how you think about a “good guess” for a parameter; we focus on maximum likelihood and the method of moments, as well as the Newton-Raphson algorithm as an example of how to use numerical/computational methods to find estimates.

Learning goals for this module include:

• Work with maximum likelihood (ML) estimators
  • Explain what a maximum likelihood estimator is (why is this a “good guess”?)
  • Derive the ML estimator for a particular parameter
    • Note: this is an example of something that can get Kind Of Involved, computationally speaking. For topics like this, you often do more elaborate examples on the Practice Problems, but on a time-limited Assessment I would not ask you to do super extensive algebra/calculus computation. You might be asked to set up a formula or describe the process, or you might have to work out a shorter/simpler example.
• Work with method of moments (MoM) estimators
  • Explain what a MoM estimator is and why it’s a “good guess”
  • Derive the MoM estimator for a particular parameter (or in some cases, just explain the process of doing so – see note above)
• Work with the Newton-Raphson algorithm, as an example of numerical optimization
  • Explain what this is (in the context of numerical methods in general) and why you might need to use it
  • Describe the procedure of the algorithm itself