Related papers: Functional principal component analysis for functi…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
Asymptotic inference using functional principal component regression (FPCR) has long been considered difficult, largely because, upon any scalar scaling, the FPCR estimator fails to satisfy a central limit theorem, leading to the prevailing…
Clinical biosensors with low detection limit hold significant promise in the early diagnosis of debilitating diseases. Recent progress in sensor development has led to the demonstration of detection capable of detecting target molecules…
Marginal structural models (MSMs) are commonly used to estimate causal intervention effects in longitudinal non-randomised studies. A common issue when analysing data from observational studies is the presence of incomplete confounder data,…
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…
Many analyses of functional magnetic resonance imaging (fMRI) examine functional connectivity (FC), or the statistical dependencies among distant brain regions. These analyses are typically exploratory, guiding future confirmatory research.…
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…
Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…
Modeling non-linear temporal trajectories is of fundamental interest in many application areas, such as in longitudinal microbiome analysis. Many existing methods focus on estimating mean trajectories, but it is also often of value to…
Principal Component Analysis (PCA) is one of the most used tools for extracting low-dimensional representations of data, in particular for time series. Performances are known to strongly depend on the quality (amount of noise) and the…
The extraordinary advancements in neuroscientific technology for brain recordings over the last decades have led to increasingly complex spatio-temporal datasets. To reduce oversimplifications, new models have been developed to be able to…
The regression of principal component scores (RPCS) on covariates is a widely used analytic approach to detect and test for associations between functional measurements and study participant characteristics. Here we show that: (1) RPCS…
Many agent based simulation approaches have been proposed for pedestrian flow. As such models are applied e.g.\ in evacuation studies, the quality and reliability of such models is of vital interest. Pedestrian trajectories are functional…
This paper treats a blind detection problem to identify the central nodes in a graph from filtered graph signals. Unlike prior works which impose strong restrictions on the data model, we only require the underlying graph filter to satisfy…
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…
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…
Existing approaches for multivariate functional principal component analysis are restricted to data on the same one-dimensional interval. The presented approach focuses on multivariate functional data on different domains that may differ in…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…