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We propose a new copula model for replicated multivariate spatial data. Unlike classical models that assume multivariate normality of the data, the proposed copula is based on the assumption that some factors exist that affect the joint…
The assumption of normality has underlain much of the development of statistics, including spatial statistics, and many tests have been proposed. In this work, we focus on the multivariate setting and first review the recent advances in…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
In public health applications, spatial data collected are often recorded at different spatial scales and over different correlated variables. Spatial change of support is a key inferential problem in these applications and have become…
Multivariate analysis of variance (MANOVA) is a powerful and versatile method to infer and quantify main and interaction effects in metric multivariate multi-factor data. It is, however, neither robust against change in units nor a…
Registration of multivariate functional data involves handling of both cross-component and cross-observation phase variations. Allowing for the two phase variations to be modelled as general diffeomorphic time warpings, in this work we…
We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…
Air pollution remains a critical environmental and public health challenge, demanding high-resolution spatial data to better understand its spatial distribution and impacts. This study addresses the challenges of conducting multivariate…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…
With the rapid development of location based services, multimodal spatio-temporal (ST) data including trajectories, transportation modes, traffic flow and social check-ins are being collected for deep learning based methods. These deep…
Multivariate functional data has received considerable attention but testing for equality of mean surfaces and its profile has limited progress. The existing literature has tested equality of either mean curves of univariate functional…
Most existing literature focuses on the exterior temporal rhythm of human movement to infer the functional regions in a city, but they neglects the underlying interdependence between the functional regions and human activities which…
We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally…
Current statistical inference problems in areas like astronomy, genomics, and marketing routinely involve the simultaneous testing of thousands -- even millions -- of null hypotheses. For high-dimensional multivariate distributions, these…
We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional…
We introduce the functional mean-shift algorithm, an iterative algorithm for estimating the local modes of a surrogate density from functional data. We show that the algorithm can be used for cluster analysis of functional data. We propose…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
Air pollution remains a major environmental risk factor that is often associated with adverse health outcomes. However, quantifying and evaluating its effects on human health is challenging due to the complex nature of exposure data. Recent…
We propose a new method for clustering of functional data using a $k$-means framework. We work within the elastic functional data analysis framework, which allows for decomposition of the overall variation in functional data into amplitude…
Effective methods for visualizing data involving multiple variables, including categorical ones, are limited. The hammock plot (Schonlau 2003) visualizes both categorical and numerical variables using parallel coordinates. We introduce the…