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Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…

Methodology · Statistics 2012-12-27 Tomokazu Konishi

We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…

Methodology · Statistics 2021-06-18 Haozhe Zhang , Yehua Li

Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements $X$ in $L^2[0,1]$. We place ourselves in a…

Statistics Theory · Mathematics 2023-08-03 Stephan Clémençon , Nathan Huet , Anne Sabourin

We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These…

Econometrics · Economics 2025-02-26 Sven Otto , Nazarii Salish

Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…

Applications · Statistics 2013-04-26 Haochang Shou , Vadim Zipunnikov , Ciprian M. Crainiceanu , Sonja Greven

Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…

Methodology · Statistics 2025-03-25 Nuwan Weeraratne , Lyn Hunt , Jason Kurz

As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…

Statistics Theory · Mathematics 2020-07-08 Israel Martínez-Hernández , Marc G. Genton

We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…

Statistics Theory · Mathematics 2014-05-26 Li Wang , Lan Xue , Annie Qu , Hua Liang

Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…

Methodology · Statistics 2020-08-21 Xiaoke Zhang , Wu Xue , Qiyue Wang

We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…

Methodology · Statistics 2021-08-10 Karl Oskar Ekvall

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

Statistics Theory · Mathematics 2010-03-02 Ci-Ren Jiang , Jane-Ling Wang

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric…

Methodology · Statistics 2008-01-17 Ping Ma , Wenxuan Zhong

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…

Methodology · Statistics 2023-05-26 Lingxuan Shao , Fang Yao

We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…

Econometrics · Economics 2020-05-12 Tobias Hartl

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Machine Learning · Computer Science 2019-10-14 Jochen Görtler , Thilo Spinner , Dirk Streeb , Daniel Weiskopf , Oliver Deussen

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…

Methodology · Statistics 2021-01-01 Clara Happ , Fabian Scheipl , Alice-Agnes Gabriel , Sonja Greven

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…

Methodology · Statistics 2023-06-27 Hossein Haghbin , Yue Zhao , Mehdi Maadooliat

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…

Statistics Theory · Mathematics 2013-01-22 Bo Markussen

Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…

Applications · Statistics 2009-01-26 Dorin Drignei , Chris E. Forest , Doug Nychka

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…

Methodology · Statistics 2025-03-10 Jiazhen Xu , Andrew T. A. Wood , Tao Zou