相关论文: A geometric framework for asymptotic inference of …

This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…

In econometrics, many parameters of interest can be written as ratios of expectations. The main approach to construct confidence intervals for such parameters is the delta method. However, this asymptotic procedure yields intervals that may…

A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotically harmonic manifolds include flat spaces and rank one…

This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

We begin a systematic study of these spaces, initially following along the lines of Eberlein's comprehensive study of the Riemannian case. In particular, we integrate the geodesic equation, discuss the structure of the isometry group, and…

In this paper we establish asymptotic simultaneous confidence bands for copulas based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the copula function, a uniform in…

We address shortcomings of principal component analysis (PCA) for visualizing high-dimensional data lying on a nonlinear low-dimensional manifold via two-dimensional scatterplots, focusing on a fossil teeth dataset from the early mammalian…

We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…

Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…

Construction of tight confidence regions and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence regions for categorical data. More precisely, consider…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

In this paper, we begin by constructing global linear maps on (n-2)-dimensional subspaces, derived from the local continuity of linear transformations among central sections of a convex body. Using these linear maps, we subsequently…

This paper studies the uniformly asymptotic stability of nonautonomous systems on Riemannian manifolds. We establish corresponding Lyapunov-type theorems (Theorems 2.1 and 2.2), extending classical Euclidean results (e.g., [9, Theorems 4.9…

In many CAD-based applications, complex geometries are defined by a high number of design parameters. This leads to high-dimensional design spaces that are challenging for downstream engineering processes like simulations, optimization, and…

Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…

Asymptotic uniform confidence bands are constructed for a multivariate nonparametric regression model with heteroscedastic noise, employing histogram estimators under flexible partition conditions. The construction is especially applicable…

Computing size and credibility of Bayesian credible regions for certifying the reliability of any point estimator of an unknown parameter (such as a quantum state, channel, phase, \emph{etc.}) relies on rejection sampling from the entire…

Recent advances in computer vision and machine learning suggest that a wide range of problems can be addressed more appropriately by considering non-Euclidean geometry. In this paper we explore sparse dictionary learning over the space of…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…