多元高斯分布的最广泛使用的属性之一，除了它的尾部行为，是条件均值是线性的，条件方差是常数。我们在这里表明，这种属性也是共享的，在近似意义上，由一大类非高斯分布。我们考虑了几个条件变量，并提供了明确的非渐近结果，从而扩展了Hall and Li（1993）和Leeb（2013）的早期发现。
英文摘要：
One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also shared, in an approximate sense, by a large class of non-Gaussian distributions. We allow for several conditioning variables and we provide explicit non-asymptotic results, whereby we extend earlier findings of Hall and Li (1993) and Leeb (2013).
On the conditional distributions of low-dimensional projections from high-dimensional data
我们研究了高维数据的低维投影的条件分布，条件是在其他低维投影上。为了解决这个问题，考虑一个随机d向量Z，它具有勒贝格密度，并且被标准化，使得$\mathbb{E}Z=0$和$\mathbb{E}ZZ'=I_d$。此外，考虑由单位向量$α$和$β$定义的两个投影，即响应$y=α'Z$和解释变量$x=β'Z$。我们早就知道，只要Z的维数很大，给定x的y的条件平均值在x $ under some regularity conditions; cf. Hall and Li [Ann. Statist. 21 (1993) 867-889]. However, a corresponding result for the conditional variance has not been available so far. We here show that the conditional variance of y given x is approximately constant in x (again, under some regularity conditions). These results hold uniformly in $ α $ and for most $ β中近似线性。从这个意义上说，我们看到高维整体模型的大多数线性子模型都是近似正确的。我们的研究结果为各种建模…
Negative Moment Bounds for Sample Autocovariance Matrices of Stationary Processes Driven by Conditional Heteroscedastic Errors and Their Applications
Institute of Statistical Science, Academia Sinica（中央研究院统计科学研究所）；Institute of Statistics and Data Science, National Tsing Hua University（国立清华大学统计与数据科学研究所）；Institute of Statistics, National University of Kaohsiung（高雄大学统计研究所）
Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机过程研究所）；Eidgenössische Technische Hochschule Zürich（苏黎世联邦理工学院）
