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高维椭圆分布模型的检验AI 解读

Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings, and to the best of our knowledge, there are no established goodness-of-fit tests for elliptical models that are supported by theoretical guarantees in high dimensions. In this paper, we propose a new goodness-of-fit test for this problem,…

基于 Bootstrap 的高维多元方差分析及函数与稀疏计数数据应用AI 解读

We propose a new approach to the problem of high-dimensional multivariate ANOVA via bootstrapping max statistics that involve the differences of sample mean vectors. The proposed method proceeds via the construction of simultaneous confidence regions for the differences of population mean vectors. It is suited to simultaneously test the equality of several pairs of mean vectors of potentially more than two populations. By exploiting the variance decay property that is a…

隐式平滑下的高维中心极限定理与自助近似AI 解读

Nonasymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry–Esseen bounds for such approximations with respect to the multivariate Kolmogorov distance, in the context of a sum of n random vectors that are p-dimensional and i.i.d. Up to now, a growing line of work has established bounds with mild logarithmic dependence on p. However, the problem of developing corresponding…

高维最大值统计量的自助法：弱方差衰减下的近参数速率及应用AI 解读

In recent years, bootstrap methods have drawn attention for their ability to approximate the laws of “max statistics” in high-dimensional problems. A leading example of such a statistic is the coordinatewise maximum of a sample average of $n$ random vectors in $\mathbb{R}^{p}$. Existing results for this statistic show that the bootstrap can work when $n\ll p$, and rates of approximation (in Kolmogorov distance) have been obtained with only logarithmic dependence in $p$.…

用 Bootstrap 估计随机集成方法的算法方差AI 解读

Although the methods of bagging and random forests are some of the most widely used prediction methods, relatively little is known about their algorithmic convergence. In particular, there are not many theoretical guarantees for deciding when an ensemble is “large enough”—so that its accuracy is close to that of an ideal infinite ensemble. Due to the fact that bagging and random forests are randomized algorithms, the choice of ensemble size is closely related to the notion…