Related papers: Derivative Estimation of Multivariate Functional D…
In this paper, in a multivariate setting we derive near optimal rates of convergence in the minimax sense for estimating partial derivatives of the mean function for functional data observed under a fixed synchronous design over H\"older…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
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…
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…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…
Building upon factor decomposition to overcome the curse of dimensionality inherent in multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework. We propose a two-stage estimation…
We describe a method for approximating a single-variable function $f$ using persistence diagrams of sublevel sets of $f$ from height functions in different directions. We provide algorithms for the piecewise linear case and for the smooth…
We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…
In this article we present some statistical applications of the functional singular value decomposition (FSVD). This tool allows us to decompose the sample mean of a bivariate stochastic process into components that are functions of…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…
With modern technology development, functional data are being observed frequently in many scientific fields. A popular method for analyzing such functional data is ``smoothing first, then estimation.'' That is, statistical inference such as…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
We propose a dynamic multiplicative factor model for process data, which arise from complex problem-solving items, an emerging testing mode in large-scale educational assessment. The proposed model can be viewed as an extension of the…
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…
Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as…
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.…
Compositional data represent a specific family of multivariate data, where the information of interest is contained in the ratios between parts rather than in absolute values of single parts. The analysis of such specific data is…