Related papers: Robust Functional Data Analysis for Discretely Obs…

This paper studies linear reconstruction of partially observed functional data which are recorded on a discrete grid. We propose a novel estimation approach based on approximate factor models with increasing rank taking into account…

Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Discrete-time random walks and their extensions are common tools for analyzing animal movement data. In these analyses, resolution of temporal discretization is a critical feature. Ideally, a model both mirrors the relevant temporal scale…

Randomized smoothing has shown promising certified robustness against adversaries in classification tasks. Despite such success with only zeroth-order access to base models, randomized smoothing has not been extended to a general form of…

Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous), pain levels (truncated), mood states (ordinal), and life…

The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its…

In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…

Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…

This paper considers the problem of robustly estimating the parameters of a heavy-tailed multivariate distribution when the covariance matrix is known to have the structure of a low-rank matrix plus a diagonal matrix as considered in factor…

Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…

Traditional fault diagnosis methods struggle to handle fault data, with complex data characteristics such as high dimensions and large noise. Deep learning is a promising solution, which typically works well only when labeled fault data are…

Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…

Robust estimation approaches are of fundamental importance for statistical modelling. To reduce susceptibility to outliers, we propose a robust estimation procedure with t-process under functional ANOVA model. Besides common mean structure…

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Robust statistics aims to compute quantities to represent data where a fraction of it may be arbitrarily corrupted. The most essential statistic is the mean, and in recent years, there has been a flurry of theoretical advancement for…

In recent years, partially observable functional data has gained significant attention in practical applications and has become the focus of increasing interest in the literature. In this thesis, we build upon the concept of data…

Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…

Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough…