Parametric Inference (Parameter Estimation)
Notation.
Given a parametric model
\(\mathcal{F} = \left\{ f(x;\theta) : \theta \in \Theta \right\} ,\)
we denote
\[ \mathbb{P}(X \in A ) = \int_A f(x;\theta) \, dx\]
and
\[ \mathbb{E}_\theta ( r(X)) = \int r(x) f(x;\theta) \, dx \,.\]