Testing Experiments Admitting an Isotone Likelihood Quotient

Testing experiments with an isotone likelihood quotient arise whenever one considers a special class of parametrized experiments (Ω,A, P; χ: P→IR) and investigates those testing experiments (Ω,A, PP₀,P₁) which are consistent with the given parametrization. Here, parametrizations are understood to be infective mappings χ: P+IR. We shall put θ: = χ (P), and for every θ ∈ Θ we write P_θ: = χ−1(θ). In this context, the mapping β_t: Θ → [0,1] defined by $$ {\beta_t}(\theta ): = \int t \,d{P_{\theta }} = {E_{\theta }}(t) $$ for all θ ∈ Θ appears to be the power function of the test t ∈ℳ₍₁₎ (Ω, A).