Decision-Theoretic Foundations of Statistical Inference

Abstract

Considering that the overall purpose of most inferential studies is to provide the statistician (or a client) with a decision,it seems reasonable to ask for an evaluation criterion of decision procedures which assesses the consequences of each decision and depends on the parameters of the model, i.e., the true state of the “world” (or of “Nature”). These decisions can be of various kinds, ranging from buying stock market shares depending on their future returns θ to stopping an agriculture experiment on the productivity θ of a new crop species, and including estimation of the underground economy contribution to the U.S. GNP, θ, or deciding whether the number θ of homeless people has increased since the last census.