Chapter 4 M4: Estimator behavior

Having established some ways to create estimators, in this module we dig in on how those estimators actually behave. Do they…work? How well? What happens if we have a really big sample to base them on? These questions turn out to underlie the inference tools you’ve been working with your whole statistical life, so there’s a lot to say about them :)

Learning goals for this module include:

• Describe an estimator’s bias, variance, and MSE (mean squared error)
  • …which includes talking about what those things are (what do they say about the estimator and the estimates it gives you?), but also actually finding them given a specific example
• Describe the Fisher information associated with an estimator
  • Again, this involves both being able to explain what Fisher information is/does (what is it for?), and actually finding it.
  • As always, Assessments won’t involve super-complicated algebra (or you might just have to set things up and not calculate it all out).
  • This includes both regular and observed Fisher information!
• Find large-sample distributions for estimators
  • Particularly for MLEs!
• Explain and assess consistency, efficiency, and the Cramer-Rao Lower Bound (CRLB)
  • This includes defining/explaining each one separately (what does it say? why is that useful?), but also explaining how they relate to each other.
  • The “and assess” part means you can actually determine whether a given estimator displays these properties!