Inference for the Crossing Point of Two Continuous CDF's
两个连续分布函数交叉点的统计推断
Let $\mathscr{F}$ denote the set of cdf's on $\mathbb{R}$ with density everywhere positive. Let $C_A = \{(F,G) \in \mathscr{F} \times \mathscr{F}$: there exists a unique $x^\ast \in \mathbb{R}$ such that $F(x) > G(x) \text{for} x << x^\ast \text{and} F(x) < G(x) \text{for} x > x^\ast\}, C_B - \{(F,G) \in \mathscr{F} \times \mathscr{F}: (G,F) \in C_A\}$. Based on independent random samples from $F$ and $G$ (assumed unknown), we give distribution-free tests of $H_0: F = G$ vers…