Related papers: Covariate adjusted functional principal components…
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…
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…
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…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…
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…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
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…
Principal component analysis and factor analysis are fundamental multivariate analysis methods. In this paper a unified framework to connect them is introduced. Under a general latent variable model, we present matrix optimization problems…
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…
A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the…
Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data…
We present a new method based on Functional Data Analysis (FDA) for detecting associations between one or more scalar covariates and a longitudinal response, while correcting for other variables. Our methods exploit the temporal structure…
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…
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…
In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to…
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…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…