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随机对象的关联度量与独立性检验AI 解读

We develop a unified framework for testing independence and quantifying association between random objects that are located in general metric spaces. Special cases include functional and high-dimensional data as well as networks, covariance matrices and data on Riemannian manifolds, among other metric space-valued data. A key concept is the profile association, a measure based on distance profiles that intrinsically characterize the distributions of random objects in metric…

重复测量数据的深度回归AI 解读

Nonparametric mean function regression with repeated measurements serves as a cornerstone for many statistical branches, such as longitudinal/panel/functional data analysis. In this work, we investigate this problem using fully connected deep neural network (DNN) estimators with flexible shapes. A novel theoretical framework allowing arbitrary sampling frequency is established by adopting empirical process techniques to tackle clustered dependence. We then consider the DNN…

离散观测数据的函数主成分分析理论AI 解读

Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on eigen-decomposition plays a central role for data reduction and representation. After nearly three decades of research, there remains a key problem unsolved, namely, the perturbation analysis of covariance operator for diverging number of eigencomponents…

随机对象的共形推断AI 解读

We develop an inferential tool kit for analyzing object-valued responses, which correspond to data situated in general metric spaces, paired with Euclidean predictors within the conformal framework. To this end, we introduce conditional profile average transport costs, where we compare distance profiles that correspond to one-dimensional distributions of probability mass falling into balls of increasing radius through the optimal transport cost when moving from one distance…

离散观测数据的函数型线性回归：从理想到现实AI 解读

Summary Despite extensive studies on functional linear regression, there exists a fundamental gap in theory between the ideal estimation from fully observed covariate functions and the reality that one can only observe functional covariates discretely with noise. The challenge arises when deriving a sharp perturbation bound for the estimated eigenfunctions in the latter case, which renders existing techniques for functional linear regression not applicable. We use a pooling…