14.5 Estimation

• We have the tools to use data to infer information about the (joint) distribution

• Because the joint distribution is complicated, we’ll usually estimate simpler summaries of the joint distribution – e.g. \(E[X]\), \(V[X]\), \(E[Y|X]\), \(Cov[X,Y]\)

• There are a number of techniques that you can use to develop an estimator for a parameter. These techniques vary in terms of the principle used to arrive at the estimator and the strength of the assumptions needed to support it.

• However, all of these estimators are statistics meaning they are functions of the data \(\{X_i\}_{i=1}^n\)