Questions tagged [neyman-pearson-lemma]

I am trying to understand Neyman Pearson Lemma's proff from Rice's book. The lemma is intuitive, however I am not able to understand the reasoning for the first inequality in the proof. I highlighted their reasoning (just below the inequality), but…

I'm unsure why, given a uniformly most powerful test exists, that the Neyman-Pearson lemma delivers the same critical region for all $\theta_1\in \Omega_1.$ Is it because this is the smallest critical region?

I cannot understand this statement from the book Robust Statistics: The most powerful tests between two densities $p_0$ and $p_1$, are based on a statistic of the form $$\int \psi F_n(dx) = \frac{1}{n}\Sigma \psi (x_i), \text{ where } \psi(x) =…

My $f(x) = \theta x ^{ (\theta -1)}$ for $0 < x < 1$ and $\theta > 0$. I found that the UMP to test $H_0: \theta = 1 \mbox{ vs } H_a: \theta = \theta_a$ is $\sum(ln(x_i)) \geq c$. I have a total of n= 50. Now I want to find the c for which I get a…