Related papers: Estimation of Multivariate Functional Principal Co…
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…
This study presents the development of multivariate functional Moran's I, along with a novel approach termed multivariate functional areal spatial principal component analysis (mfasPCA), specifically designed for analyzing functional areal…
Aggregating multi-subject functional magnetic resonance imaging (fMRI) data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional…
This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…
Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
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…
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…
Modern longitudinal studies collect multiple outcomes as the primary endpoints to understand the complex dynamics of the diseases. Oftentimes, especially in clinical trials, the joint variations among the multidimensional responses play a…
We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…
Human mortality patterns and trajectories in closely related populations are likely linked together and share similarities. It is always desirable to model them simultaneously while taking their heterogeneity into account. This paper…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However,…
Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
We propose a new method for modelling simple longitudinal data. We aim to do this in a flexible manner (without restrictive assumptions about the shapes of individual trajectories), while exploiting structural similarities between the…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
In clinical practice and biomedical research, measurements are often collected sparsely and irregularly in time while the data acquisition is expensive and inconvenient. Examples include measurements of spine bone mineral density, cancer…
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…