Related papers: Functional Principal Components Analysis of Spatia…
In this paper, we propose a novel model to analyze serially correlated two-dimensional functional data observed sparsely and irregularly on a domain which may not be a rectangle. Our approach employs a mixed effects model that specifies the…
We introduce a new class of conditional autoregressive models for spatially dependent functional data, formulated through conditional means given neighboring functional observations and characterized by a covariance operator and a spatial…
We propose an estimation approach to analyse correlated functional data which are observed on unequal grids or even sparsely. The model we use is a functional linear mixed model, a functional analogue of the linear mixed model. Estimation…
This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\mathbf{s}_k;t),t\in[0,T]$,…
The idea of spatial crosscorrelation was conceived of long ago. However, unlike the related spatial autocorrelation, the theory and method of spatial crosscorrelation analysis have remained undeveloped. This paper presents a set of models…
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
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 this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and…
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…
We introduce a spatial function-on-function regression model to capture spatial dependencies in functional data by integrating spatial autoregressive techniques with functional principal component analysis. The proposed model addresses a…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…
Spatial autocorrelation coefficients such as Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…