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多层随机点积图：估计与在线变点检测AI 解读

Abstract We study the multilayer random dot product graph (MRDPG) model, a generalization of the random dot product graph model to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework, where, at each time point, we observe a realization from an MRDPG. Across layers, we assume fixed…

高维潜在面板分位数回归及其资产定价应用AI 解读

We propose a generalization of the linear panel quantile regression model to accommodate both sparse and dense parts: sparse means that while the number of covariates available is large, potentially only a much smaller number of them have a nonzero impact on each conditional quantile of the response variable; while the dense part is represent by a low-rank matrix that can be approximated by latent factors and their loadings. Such a structure poses problems for traditional…

分位数趋势滤波的风险界AI 解读

Summary We study quantile trend filtering, a recently proposed method for nonparametric quantile regression, with the goal of generalizing existing risk bounds for the usual trend-filtering estimators that perform mean regression. We study both the penalized and the constrained versions, of order $r \geqslant 1$, of univariate quantile trend filtering. Our results show that both the constrained and the penalized versions of order $r \geqslant 1$ attain the minimax rate up to…