Related papers: Basis Expansions for Functional Snippets

Area-specific causal inference is important in many policy and survey applications, where the goal is to evaluate treatment effects for small geographic or demographic domains. Existing causal small area estimation methods, however,…

We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology…

Functional data analysis has been a growing field of study in recent decades, and one fundamental task in functional data analysis is estimating the sample location. A notion called statistical depth has been extended from multivariate data…

Dimension reduction is often necessary in functional data analysis, with functional principal component analysis being one of the most widely used techniques. A key challenge in applying these methods is determining the number of…

We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression…

Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…

We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…

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…

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…

Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study…

In this paper, we study the estimation and inference of change points under a functional linear regression model with changes in the slope function. We present a novel Functional Regression Binary Segmentation (FRBS) algorithm which is…

In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…

We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…

This article deals with the problem of functional classification for L2-valued random covariates when some of the covariates may have missing or unobservable fragments. Here, it is allowed for both the training sample as well as the new…

We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…

We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…

Conformal prediction is a theoretically grounded framework for constructing predictive intervals. We study conformal prediction with missing values in the covariates -- a setting that brings new challenges to uncertainty quantification. We…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…