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基于随机投影经验过程的函数型线性模型拟合优度检验AI 解读

We consider marked empirical processes indexed by a randomly projected functional covariate to construct goodness-of-fit tests for the functional linear model with scalar response. The test statistics are built from continuous functionals over the projected process, resulting in computationally efficient tests that exhibit root-$n$ convergence rates and circumvent the curse of dimensionality. The weak convergence of the empirical process is obtained conditionally on a random…

DD 分类器：基于深度对深度图的非参数分类方法AI 解读

Using the DD-plot (depth vs. depth plot), we introduce a new nonparametric classification algorithm and call it DD-classifier. The algorithm is completely nonparametric, and it requires no prior knowledge of the underlying distributions or the form of the separating curve. Thus, it can be applied to a wide range of classification problems. The algorithm is completely data driven and its classification outcome can be easily visualized in a two-dimensional plot regardless of…

修剪与似然：椭圆模型中的稳健位置及离散程度估计AI 解读

Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here we analyze some one (or k)-step Maximum Likelihood Estimators computed on a subsample obtained with such a procedure. We introduce different models which arise naturally from the ways in which the discarded data can be treated, leading to…

基于 L₂-Wasserstein 距离的拟合优度检验AI 解读

We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance we obtain a version of Shapiro–Wilk’s test of normality. The asymptotic behavior of the statistic is studied using approximations of the quantile process by Brownian bridges. This method differs from the “ad hoc” method of de Wet and Venter and permits a similar analysis for testing other…