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第二类删失样本的渐近卡方正态性检验AI 解读

A method is proposed for testing normality, in the case of general Type II censored data—that is, data for which only a subset of the order statistics are available. Three test statistics are proposed, which are generalizations of the statistics proposed in LaRiccia (1986), and have many of the same properties. Specifically, they are designed to be asymptotically optimal with respect to specific alternatives and are easily adjusted to be asymptotically optimal with respect…

第二类删失样本的渐近卡方正态性检验AI 解读

A method is proposed for testing normality, in the case of general Type II censored data—that is, data for which only a subset of the order statistics are available. Three test statistics are proposed, which are generalizations of the statistics proposed in LaRiccia (1986), and have many of the same properties. Specifically, they are designed to be asymptotically optimal with respect to specific alternatives and are easily adjusted to be asymptotically optimal with respect…

一类最小分位数距离估计量的渐近性质AI 解读

A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M…

一族最小分位数距离估计量的渐近性质AI 解读

A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M…

基于 L 统计量平方和的位置—尺度分布族最优拟合优度检验AI 解读

A class of goodness-of-fit tests based on sums of squares of $L$-statistics is proposed for testing a composite parametric location and/or scale null hypothesis versus a general parametric alternative. It is shown that such tests can be constructed optimally to have the same asymptotic power against sequences of local alternatives as the generalized likelihood ratio statistics [G.L.R.S.] and, in fact, under suitable regularity conditions to be asymptotically equivalent to…

加权 L² 分位数距离估计量的渐近性质AI 解读

The asymptotic properties of a family of minimum quantile function distance estimators are considered. These procedures take as the parameter estimates that vector which minimizes a weighted $L^2$ distance between the empirical quantile function and an assumed parametric family of quantile functions. Regularity conditions needed for these estimators to be consistent and asymptotically normal are presented. For single parameter families of distributions, the optimal form of…