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Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Methodology · Statistics 2025-07-15 Felix Reinbott , Anja Janßen

We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and…

Statistics Theory · Mathematics 2020-09-04 Joni Virta , Bing Li , Klaus Nordhausen , Hannu Oja

We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…

Methodology · Statistics 2023-10-04 Angel Garcia de la Garza , Britton Sauerbrei , Adam Hantman , Jeff Goldsmith

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…

Methodology · Statistics 2024-10-07 Peijun Sang , Dehan Kong , Shu Yang

Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…

Statistics Theory · Mathematics 2013-02-26 Stefan Fremdt , Lajos Horváth , Piotr Kokoszka , Josef G. Steinebach

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

Machine Learning · Statistics 2020-12-10 Michael Weylandt

Matrix factor model has been growing popular in scientific fields such as econometrics, which serves as a two-way dimension reduction tool for matrix sequences. In this article, we for the first time propose the matrix elliptical factor…

Methodology · Statistics 2022-03-29 ZeYu Li , Yong He , Xinbing Kong , Xinsheng Zhang

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

Methodology · Statistics 2018-01-08 Jianqing Fan , Qiang Sun , Wen-Xin Zhou , Ziwei Zhu

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…

Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. In this study, we analyze minute-level indicators of being active,…

Methodology · Statistics 2025-04-01 Xinkai Zhou , Julia Wrobel , Ciprian M. Crainiceanu , Andrew Leroux

Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…

Methodology · Statistics 2024-06-04 Merle Munko , Marc Ditzhaus , Markus Pauly , Łukasz Smaga

The Sleep Heart Health Study (SHHS) is a comprehensive landmark study of sleep and its impacts on health outcomes. A primary metric of the SHHS is the in-home polysomnogram, which includes two electroencephalographic (EEG) channels for each…

Applications · Statistics 2009-06-09 Chong-Zhi Di , Ciprian M. Crainiceanu , Brian S. Caffo , Naresh M. Punjabi

Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…

Machine Learning · Statistics 2018-08-24 Clifford Anderson-Bergman , Tamara G. Kolda , Kina Kincher-Winoto

We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a…

Statistics Theory · Mathematics 2025-11-05 Franck Picard , Vincent Rivoirard , Angelina Roche , Victor Panaretos

Functional data analysis on nonlinear manifolds has drawn recent interest. Sphere-valued functional data, which are encountered for example as movement trajectories on the surface of the earth, are an important special case. We consider an…

Statistics Theory · Mathematics 2017-10-25 Xiongtao Dai , Hans-Georg Müller

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…

Methodology · Statistics 2025-04-15 Jiarui Zhang , Jiguo Cao , Liangliang Wang

Current functional Magnetic Resonance Imaging technology is able to resolve billions of individual functional connections characterizing the human connectome. Classical statistical inferential procedures attempting to make valid inferences…

Quantitative Methods · Quantitative Biology 2023-01-11 Alfonso Nieto-Castanon

In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…

Methodology · Statistics 2026-04-27 Xinyu Zhang , Ameer Qaqish , D. Y. Lin , Didong Li

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Optimization and Control · Mathematics 2025-12-02 Ryan Cory-Wright , Jean Pauphilet

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…

Methodology · Statistics 2015-08-20 Vincent Audigier , François Husson , Julie Josse