Monday, March 4, 2013

Measuring the Quality of an Estimator

In which, with almost no symbols, I encourage students and practitioners to question what they've been taught............

When it comes to introducing our students to the notion of the "quality" of an estimator, most of us begin by observing that estimators are functions of the random sample data, and hence they are "statistics" in the literal sense. As such, estimators have a probability distribution. We give this distribution a special name - the "sampling distribution" of the estimator in question.

It's understandable that students sometimes find the concept of the sampling distribution a little tricky when they first encounter it. After all, it's based on a "thought game" of sorts. We have to consider the idea of repeatedly drawing samples of a fixed size, for ever, constructing the statistic in question, and then keeping track of all of the possible values that the statistic can take, together with the relative frequency of occurrence for each value. A Monte Carlo experiment is the obvious way to introduce students to this concept.