Related papers: Robust Functional Principal Component Analysis for…
Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenall's $\tau$ function, which possesses…
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…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
This paper examines robust functional data analysis for discretely observed data, where the underlying process encompasses various distributions, such as heavy tail, skewness, or contaminations. We propose a unified robust concept of…
The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…
Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…
Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
Recent advances have sparked significant interest in the development of privacy-preserving Principal Component Analysis (PCA). However, many existing approaches rely on restrictive assumptions, such as assuming sub-Gaussian data or being…
In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…
This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been…
Modern mobile health (mHealth) assessment combines self-reported measures of participants' health experiences with passively collected health behavior data throughout the day. These data are collected across multiple measurement scales,…