Unbiased Test

Definition

Let

• $X$ : Random variable with pdf/pmf $f(x;\theta ),\theta \in \Omega$
• ${\mathbf{X}}^{\prime }=(X_1,\dots ,X_n)$ : Random sample on $X$

Consider

• Hypotheses $H_0:\theta \in {\omega }_0$ versus $H_1:\theta \in {\omega }_1$
• A test with critical region $C$ and significance level $\alpha$

If $P_{\theta }(\mathbf{X}\in C)\ge \alpha ,\forall \theta \in {\omega }_1$

Then we say that this test is unbiased

Related

• Neyman-Pearson Theorem