An Introduction to Probability and Statistical Inference, 2nd Edition

9.4 Decision-Theoretic Approach to Estimation

In this section, a brief discussion is presented of still another approach to parameter estimation, which, unlike the previous two approaches, is kind of penalty driven. In order to introduce the relevant concepts and notation, let X₁, …, X_n be a random sample with p.d.f. $f\left(\cdot ;\theta \right),\theta \in \Omega \subseteq \text{ℜ}$, and let δ be a function defined on ${\text{ℜ}}^n$ into Ω; i.e., δ : ${\text{ℜ}}^n\to \Omega$. If x₁, …, x_n are the observed values of X₁, …, X_n, then ...