12.1 Confidence functions
In order to construct confidence regions (i.e. subsets Θ1−α of the parameter space Θ) which contain the true parameter θ0 with high probability 1 − α (where α is a very small positive number) so-called confidence functions are used. A confidence function
is a function which assigns to every sample x1,…, xn a subset Θ1−α of Θ such that for a mathematical sample X1,…, Xn of the observed stochastic quantity X the following is true:
For α a value of 0.05 or 0.01 is usually taken. Therefore the so-called coverage probability is 1 − α.