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非独立同分布情形下多元线性秩统计量的渐近正态性AI 解读

Asymptotic normality is established for multivariate linear rank statistics of general type in the non-i.i.d. case covering null hypotheses as well as almost arbitrary alternatives. The functions generating the regression constants and the scores are allowed to have a finite number of discontinuities of the first kind, and to tend to infinity near 0 and 1. The proof is based on properties of empirical df's in the non-i.i.d. case and is patterned on the 1958 Chernoff-Savage…

关于随机单元边界卡方统计量的一则札记AI 解读

Moore (1971) derives the limiting distribution of chi-square statistics for testing goodness of fit to k-variate parametric families, where the cell boundaries are allowed to be functions of the estimated parameter values. The only point at which random cells, multivariate observations etc. require a deviation from methods of proof given by Cramer (1946) is in the proof of the asymptotic negligibility of the remainder terms. Attention is drawn to an alternative proof of this…

非参数独立性检验的渐近正态性AI 解读

Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established both under fixed alternatives (or the null hypothesis) and under converging alternatives. The results of Ruymgaart, Shorack and van Zwet [14] are used to obtain a further weakening of the smoothness conditions on the score functions. In the present case the score functions are allowed to have a finite number of discontinuities of the first kind. The results of the present…