Estimator Consistency in a General Setup

Abstract

Many problems considered and investigated in statistics follow a general schema. Observed data are generated by a model containing randomness and determined via a collection of parameters. We are interested in future behavior of observed system. Therefore, a convenient estimation procedure for unknown parameters becomes to be the crucial task. This schedule often leads to derivation of an optimization problem that solution is a reasonable estimator of required parameters. We are discussing behavior of such an estimator with a relatively general background. The setup is illustrated on a linear regression model.