Chapter 3 Evaluating Point Estimates

In this chapter, I discuss three concepts that we can use to evaluate an estimator from a frequentist perspective.

1. Bias
2. Consistency
3. MVUE or BUE

As a running example, we have the toothpaste cap problem and the following estimators of the chance of getting a top.

1. posterior mean: \(\hat{\pi}^{Bayes} = \dfrac{\alpha^\prime}{\alpha^\prime + \beta^\prime} = \dfrac{\alpha^* + k}{[\alpha^* + k] + [\beta^* + (N - k)]} = \dfrac{\alpha^* + k}{\alpha^* + \beta^* + N }\)
2. method of moments estimator: \(\hat{\pi}^{MM} = \frac{k}{n}\)
3. maximum likelihood estimator: \(\hat{\pi}^{ML} = \frac{k}{n}\)

For each of these estimators we can ask:

1. Is it good? (in an absolute sense)
2. Is it better than another estimator?