On the Asymptotic Formula for the Probability of a Type I Error of Mixture Type Power One Tests
On the Asymptotic Formula for the Probability of a Type I Error of Mixture Type Power One Tests
Let $X_1,X_2,\cdots$ be iid with density $f_y$ with respect to a sigma finite measure $\mu$ where ${f_y}_(y\in\omega$, $\omega\subseteqR$ is an exponential family. Let F be a probability measure on $\omega$ and let $\theta_0\in\omega$. Define $T(B,F)=\min \big\{n \left| \int_omega \frac{f_y(X_1) \1dots f_y(X_n)} {f_{\theta_0}(X_1)\dots f_{\theta_0 (X_1) \1dots f_{\theta_0} (X_n)} dF(y)\geq B \big\}$, …