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Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets.…
We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation…
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…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
A new method is proposed to perform joint analysis of longitudinal and cross-sectional growth data. Clustering is first performed to group similar subjects in cross-sectional data to form a pseudo longitudinal data set, then the pseudo…
The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…
The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Many conventional statistical and machine learning methods face challenges when applied directly to high dimensional temporal observations. In recent decades, Functional Data Analysis (FDA) has gained widespread popularity as a framework…