发表机构
Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对非负随机变量的单侧均值假设检验，提出留一法对偶证书框架，构造出更有效的p值，证明其最优性并通过实验验证功效提升。
AI 中文摘要
我们针对非负随机变量，研究单侧均值假设H₀:μ≤1对H₁:μ>1的有限样本有效检验。为此，我们提出留一法对偶证书框架，其中特定逐点不等式在条件均值原假设E[X_i|X_{-i}]≤1下蕴含p值有效性，且该框架还给出将对偶证书组合为p值的条件，证明其逐点最小值也为有效p值。该框架证明了Wang和Zhao的非参数似然比统计量T_{nplr}的有限样本有效性，得到将Clopper-Pearson二项检验扩展到一般非负随机变量的新p值T_{bin+}，并表明逐点最小值min{T_{nplr},T_{bin+}}本身是有效且更强大的p值。我们在两种情形下为这类检验问题建立了精确最优性结果：T_{nplr}和T_{bin+}均在不依赖矩或尾假设的原假设H₀下达到通用可检测边界，且T_{bin+}在H₀的n^{-1/2}-局部备择假设下达到非参数功效下界。高效算法与数值实验表明，与现有有效方法相比，该方法在有限样本下的功效有显著提升。
英文摘要
We study finite-sample valid tests of the one-sided mean hypothesis $H_0:μ\leq 1$ against $H_1:μ>1$ for nonnegative random variables. To do so, we develop a leave-one-out dual certificate framework, where certain pointwise inequalities imply p-value validity under the conditional mean null $\mathbb{E}[X_i\mid\mathbf{X}_{-i}]\leq 1$, and which also gives conditions that allow combining dual certificates for p-values to show that their pointwise minimum is also a valid p-value. The framework proves finite-sample validity of Wang and Zhao's nonparametric likelihood-ratio statistic $T_{\mathrm{nplr}}$, yields a new p-value $T_{\mathrm{bin}+}$ extending the Clopper--Pearson binomial test to general nonnegative random variables, and shows that the pointwise minimum $\min\{T_{\mathrm{nplr}},T_{\mathrm{bin}+}\}$ is itself a valid and more powerful p-value. We establish sharp optimality results for such testing problems in two regimes: both $T_{\mathrm{nplr}}$ and $T_{\mathrm{bin}+}$ attain a universal detectability boundary for the null $H_0$ without moment or tail assumptions, and $T_{\mathrm{bin}+}$ attains a nonparametric power lower bound under $n^{-1/2}$-local alternatives to $H_0$. Efficient algorithms and numerical experiments demonstrate substantial finite-sample power gains over existing valid methods.
