Uniformly More Powerful, One-Sided Tests for Hypotheses About Linear Inequalities
关于线性不等式假设的一致更有力单侧检验
Let $\mathbf{X}$ have a multivariate, $p$-dimensional normal distribution $(p \geq 2)$ with unknown mean $\mathbf{\mu}$ and known, nonsingular covariance $\mathbf{\Sigma}$. Consider testing $H_0: \mathbf{b}'_i\mathbf{\mu} \leq 0$, for some $i = 1, \ldots, k$, versus $H_1: \mathbf{b}'_i\mathbf{\mu} > 0$, for all $i = 1, \ldots, k$, where $\mathbf{b}_1, \ldots, \mathbf{b}_k, k \geq 2$, are known vectors that define the hypotheses. For any $0 < \alpha < 1/2$, we construct a…