Space-time covariance functions with compact support

关于紧致两点齐性空间上各向异性协方差函数的估计

On the Estimation of Anisotropic Covariance Functions on Compact Two-Point Homogeneous Spaces

本文将二维球面上样条型各向异性协方差估计的渐近理论推广到连通紧致两点齐性空间，拓展了该方法的适用范围。

Nonasymptotic estimation and support recovery for high dimensional sparse covariance matrices

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through incorporation of past thresholding estimators with key emphasis on support recovery. This technique goes beyond past results for thresholding estimators by allowing for a wide range of distributional assumptions beyond merely sub-Gaussian tails. This methodology can furthermore be adapted to a wide range of other estimators and settings. The usage of nonasymptotic dime…

适应性长期方差阈值法用于高维时间序列稀疏协方差估计

Adaptive Long-Run Variance Thresholding for Sparse Covariance Estimation in High-Dimensional Time Series

本文研究了弱依赖高维时间序列稀疏协方差估计，提出基于长期方差的阈值方法，实现对时间依赖性的适应，证明了估计器在谱范数下的一致性及最优收敛速度，并展示了支持恢复一致性。

稀疏紧凑支持协方差模型在高斯超几何类中的研究：可识别性、重参数化和渐近性质

Parsimonious Compactly Supported Covariance Models in the Gauss Hypergeometric Class: Identifiability, Reparameterizations, and Asymptotic Properties

本文研究高斯超几何类协方差函数，推导了有效性条件并展示了模型在固定域渐近中的结构可识别性问题，提出稀疏紧凑支持子类并通过最大积分范围准则解决，并在固定域渐近中建立了最大似然估计的强一致性和渐近正态性。

Fixed support positive-definite modification of covariance matrix estimators via linear shrinkage

In this work, we study the positive definiteness (PDness) problem in covariance matrix estimation. For high dimensional data, many regularized estimators are proposed under structural assumptions on the true covariance matrix including sparsity. They are shown to be asymptotically consistent and rate-optimal in estimating the true covariance matrix and its structure. However, many of them do not take into account the PDness of the estimator and produce a non-PD estimate. To achieve the PDness, researchers consider additional regularizations (or constraints) on eigenvalues, which make both the …

Discussion on Competition for Spatial Statistics for Large Datasets

We discuss the experiences and results of the AppStatUZH team's participation in the comprehensive and unbiased comparison of different spatial approximations conducted in the Competition for Spatial Statistics for Large Datasets. In each of the different sub-competitions, we estimated parameters of the covariance model based on a likelihood function and predicted missing observations with simple kriging. We approximated the covariance model either with covariance tapering or a compactly supported Wendland covariance function.