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两样本最优非参数得分函数的秩估计与相应自适应秩统计量AI 解读

In the general two-sample testing problem, $X_1, \cdots, X_m$ i.i.d. with continuous c.d.f. $F, Y_1, \cdots, Y_n$ i.i.d. with continuous c.d.f. $G$, and null hypothesis $H_0: F = G$ versus alternative $H_1: F \leq G, F \neq G$, we construct uniformly consistent and tractable rank estimators of the underlying optimal nonparametric score-function for a large subclass of (fixed) alternatives. Moreover, we prove asymptotic normality of the corresponding adaptive rank statistics…

作为估计得分线性秩检验的 Galton 检验及其局部渐近效率AI 解读

In the general two-sample testing problem $F = G$ versus $F \leq G, F \neq G$ the shift-model score function $f' \circ F^{-1}/f \circ F^{-1}$ has to be replaced by the nonparametric score function $b = \bar{f} - \bar{g}$, where $\bar{f} = d(F \circ H^{-1})/dx, \bar{g} = d(G \circ H^{-1})/dx, H = (mF + nG)/(m + n)$, and adaption of linear rank tests should be based on rank estimators of $b$. We consider an easy but rough and inconsistent rank estimator of $b$. The resulting…

存在并列秩时回归问题中秩检验的渐近比较AI 解读

Without assumptions on the underlying distributions we prove the asymptotic normality of averaged scores rank statistics under all product distributions which are contiguous to the null hypothesis, and find a very simple form of the centering constants. In the one-sided two-sample and trend situations this enables us to show that monotonicity of the scores generating function is equivalent to the asymptotic unbiasedness of the corresponding averaged scores rank test. For…