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高维协方差矩阵的一般线性假设检验：正态参照方法AI 解读

Statistical inference for high-dimensional data is increasingly essential due to the prevalence of big data. While recent advancements have improved testing linear hypotheses for high-dimensional mean vectors, exploration of testing linear hypotheses for high-dimensional covariance matrices remains limited. This article focuses on a general linear hypothesis testing (GLHT) problem for high-dimensional covariance matrices, encompassing various specific cases such as testing…

可分度量空间中多个分布的相等性检验：最大均值差异方法AI 解读

A new test for equal distributions of several high-dimensional samples in separable metric spaces, with its test statistic constructed based on maximum mean discrepancy, is proposed and studied. The asymptotic null and alternative distributions of the test statistic are established under some mild conditions. The new test is implemented via a three-cumulant matched chi-square approximation with the associated approximation parameters consistently estimated from the data. A…

基于 L₂ 范数的简便高维两样本检验AI 解读

Testing the equality of two means is a fundamental inference problem. For high-dimensional data, the Hotelling’s T2-test either performs poorly or becomes inapplicable. Several modifications have been proposed to address this issue. However, most of them are based on asymptotic normality of the null distributions of their test statistics which inevitably requires strong assumptions on the covariance. We study this problem thoroughly and propose an L2-norm based test that…

多个函数总体协方差函数相等性的新检验AI 解读

In this article, we propose two new tests for the equality of the covariance functions of several functional populations, namely, a quasi-GPF test and a quasi-Fmax test whose test statistics are obtained via globalizing a pointwise quasi-F-test statistic with integration and taking its supremum over some time interval of interest, respectively. Unlike several existing tests, they are scale-invariant in the sense that their test statistics will not change if we multiply each…

稀疏超高维变系数模型的前向变量选择AI 解读

Varying coefficient models have numerous applications in a wide scope of scientific areas. While enjoying nice interpretability, they also allow for flexibility in modeling dynamic impacts of the covariates. But, in the new era of big data, it is challenging to select the relevant variables when the dimensionality is very large. Recently, several works are focused on this important problem based on sparsity assumptions; they are subject to some limitations, however. We…

函数型数据的统计推断AI 解读

With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is “smoothing first, then estimation.” That is, statistical inference such as estimation and hypothesis testing about functional data is conducted based on the substitution of the underlying individual functions by their reconstructions obtained by one smoothing technique or another. However, little is known about…

卡方型混合分布的近似与渐近分布及其应用AI 解读

In this article we study how to approximate a random variable T of general chi-squared–type mixtures by a random variable of the form via matching the first three cumulants. The approximation error bounds for the density functions of the chi-squared approximation and the normal approximation are established. Applications of the results to some nonparametric goodness-of-fit tests, including those tests based on orthogonal series, smoothing splines, and local polynomial…

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函数线性模型的两步估计及其纵向数据应用AI 解读

Summary Functional linear models are useful in longitudinal data analysis. They include many classical and recently proposed statistical models for longitudinal data and other functional data. Recently, smoothing spline and kernel methods have been proposed for estimating their coefficient functions nonparametrically but these methods are either intensive in computation or inefficient in performance. To overcome these drawbacks, in this paper, a simple and powerful two-step…