Related papers: Intrinsic Riemannian Functional Data Analysis for …
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…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
In this paper, we introduce a novel statistical model for the integrative analysis of Riemannian-valued functional data and high-dimensional data. We apply this model to explore the dependence structure between each subject's dynamic…
In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…
We introduce an intrinsic estimator for the scalar curvature of a data set presented as a finite metric space. Our estimator depends only on the metric structure of the data and not on an embedding in $\mathbb{R}^n$. We show that the…
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…
We present a Riemannian framework for linear and quadratic discriminant classification on the tangent plane of the shape space of curves. The shape space is infinite dimensional and is constructed out of square root velocity functions of…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
Tracking underwater autonomous platforms is often difficult because of noisy, biased, and discretized input data. Classic filters and smoothers based on standard assumptions of Gaussian white noise break down when presented with any of…
Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…
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…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…
The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…