Properties of point estimators

Abstract

Point estimation is the attempt to identify a value associated with some underlying process or population using data. The unknown number that is the target of estimation is called an estimand. An estimator is a function that takes in data and produces an estimate. In this chapter, estimators are evaluated according to a number of criteria. An unbiased estimator is one whose expected value is equal to the estimand—in lay terms, it is accurate. Low-variance estimators, which are precise, are also evaluated. Consistent estimators converge to the estimand as the number of data collected approaches infinity. Mean squared error is the expected squared difference between the estimator and the estimand. Efficient estimators are those that converge to the estimand relatively quickly—i.e., fewer data are necessary to get close to the right answer. An optional section discusses statistical decision theory, which is a general framework for evaluating estimators. Finally, some ideas of robustness are discussed. A robust estimator is one that can still provide useful information even if the model is not quite right or the data are contaminated.