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Situations of a functional predictor paired with a scalar response are increasingly encountered in data analysis. Predictors are often appropriately modeled as square integrable smooth random functions. Imposing minimal assumptions on the…

Statistics Theory · Mathematics 2009-09-08 Peter Hall , Hans-Georg Müller , Fang Yao

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…

Statistics Theory · Mathematics 2016-08-16 Peter Hall , Hans-Georg Müller , Jane-Ling Wang

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…

Statistics Theory · Mathematics 2018-12-10 Piotr Kokoszka , Stilian Stoev , Qian Xiong

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

Functional principal components analysis is a popular tool for inference on functional data. Standard approaches rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal functions representing the…

Methodology · Statistics 2021-04-02 Tui H. Nolan , Jeff Goldsmith , David Ruppert

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

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

Functional principal component analysis is essential in functional data analysis, but the inferences will become unconvincing when some non-Gaussian characteristics occur, such as heavy tail and skewness. The focus of this paper is to…

Methodology · Statistics 2021-02-02 Rou Zhong , Shishi Liu , Jingxiao Zhang , Haocheng Li

In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over…

Applications · Statistics 2013-12-10 Gift Nyamundanda , Isobel Claire Gormley , Lorraine Brennan

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

Methodology · Statistics 2023-08-17 Xinyi Zhang , Qiang Sun , Dehan Kong

This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…

Statistics Theory · Mathematics 2014-11-19 Chong Liu , Surajit Ray , Giles Hooker

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Methodology · Statistics 2022-08-18 Xiaoyu Hu , Fang Yao

Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…

Methodology · Statistics 2024-08-20 Xiaowu Dai

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

The advance of modern sensor technologies enables collection of multi-stream longitudinal data where multiple signals from different units are collected in real-time. In this article, we present a non-parametric approach to predict the…

Machine Learning · Statistics 2023-07-04 Seokhyun Chung , Raed Kontar

Happ and Greven (2018) developed a methodology for principal components analysis of multivariate functional data observed on different dimensional domains. Their approach relies on an estimation of univariate functional principal components…

Methodology · Statistics 2025-01-28 Steven Golovkine , Edward Gunning , Andrew J. Simpkin , Norma Bargary

The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…

Machine Learning · Computer Science 2021-11-09 Chenlin Meng , Yang Song , Wenzhe Li , Stefano Ermon

Motivation: Drug discovery demands rapid quantification of compound-protein interaction (CPI). However, there is a lack of methods that can predict compound-protein affinity from sequences alone with high applicability, accuracy, and…

Biomolecules · Quantitative Biology 2020-12-17 Mostafa Karimi , Di Wu , Zhangyang Wang , Yang Shen

A new single-index model that reflects the time-dynamic effects of the single index is proposed for longitudinal and functional response data, possibly measured with errors, for both longitudinal and time-invariant covariates. With…

Statistics Theory · Mathematics 2011-03-10 Ci-Ren Jiang , Jane-Ling Wang

We demonstrate that the processes underlying on-line auction price bids and many other longitudinal data can be represented by an empirical first order stochastic ordinary differential equation with time-varying coefficients and a smooth…

Statistics Theory · Mathematics 2012-11-13 Hans-Georg Müller , Fang Yao