Related papers: Inference on common trends in functional time seri…

Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for…

This paper studies theory and inference related to a class of time series models that incorporates nonlinear dynamics. It is assumed that the observations follow a one-parameter exponential family of distributions given an accompanying…

Functional data analysis is typically conducted within the $L^2$-Hilbert space framework. There is by now a fully developed statistical toolbox allowing for the principled application of the functional data machinery to real-world problems,…

For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…

Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly…

Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…

Appealing to several multivariate information measures---some familiar, some new here---we analyze the information embedded in discrete-valued stochastic time series. We dissect the uncertainty of a single observation to demonstrate how the…

We consider a time series model involving a fractional stochastic component, whose integration order can lie in the stationary/invertible or nonstationary regions and be unknown, and an additive deterministic component consisting of a…

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…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications…

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…

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…

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…

Over the past decades, linear mixed models have attracted considerable attention in various fields of applied statistics. They are popular whenever clustered, hierarchical or longitudinal data are investigated. Nonetheless, statistical…

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…

We develop inference and testing procedures for conditional dispersion and skewness in a nonparametric regression setup based on statistical depth functions. The methods developed can be applied in situations, where the response is…