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López de Prado 与 Porcu 对《组合回归》的讨论意见AI 解读

Marcos López de Prado, Emilio Porcu; López de Prado and Porcu’s contribution to the Discussion of ‘Regression by compositio’ by Farewell et al, Journal of

Simon 等对《流形假说的统计探索》的讨论AI 解读

We congratulate the authors on their impressive effort and commend their tour de force. Our comments follow below. Theoretical foundations. The authors contribution is driven by embedding the manifold hypothesis in a rigorous statistical framework. The Latent Manifold Model (LMM) plays a central role by integrating latent variables, random functions, and structured noise within a unified construction. Grounded in Mercer’s theorem, the approach links correlation kernels with…

网络上的平稳不可分离时空协方差函数AI 解读

Abstract The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but a generalised network (termed a graph with Euclidean edges). Additionally, data are repeatedly measured over different temporal instants. We provide new classes of stationary nonseparable space-time covariance functions where…

固定域渐近下广义 Wendland 协方差函数的估计与预测AI 解读

We study estimation and prediction of Gaussian random fields with covariance models belonging to the generalized Wendland (GW) class, under fixed domain asymptotics. As for the Matérn case, this class allows for a continuous parameterization of smoothness of the underlying Gaussian random field, being additionally compactly supported. The paper is divided into three parts: first, we characterize the equivalence of two Gaussian measures with GW covariance function, and we…

球面大圆距离下的时空协方差与交叉协方差函数AI 解读

In this article, we propose stationary covariance functions for processes that evolve temporally over a sphere, as well as cross-covariance functions for multivariate random fields defined over a sphere. For such processes, the great circle distance is the natural metric that should be used to describe spatial dependence. Given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time, approximations of the state…

大型数据集的空间与时空协方差估计：加权复合似然方法AI 解读

In this article, we propose two methods for estimating space and space-time covariance functions from a Gaussian random field, based on the composite likelihood idea. The first method relies on the maximization of a weighted version of the composite likelihood function, while the second one is based on the solution of a weighted composite score equation. This last scheme is quite general and could be applied to any kind of composite likelihood. An information criterion for…