Related papers: Function-on-function Differential Regression
The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. Such estimands can typically only be estimated at a…
This paper presents tests to formally choose between regression models using different derivatives of a functional covariate in scalar-on-function regression. We demonstrate that for linear regression, models using different derivatives can…
Functional variables are often used as predictors in regression problems. A commonly-used parametric approach, called {\it scalar-on-function regression}, uses the $\ltwo$ inner product to map functional predictors into scalar responses.…
Functional data play a pivotal role across science and engineering, yet their infinite-dimensional nature makes representation learning challenging. Conventional statistical models depend on pre-chosen basis expansions or kernels, limiting…
Difference-in-differences (DiD) is a cornerstone of causal inference, yet extending it to functional outcomes is not a routine scalar generalization; rather, it entails three fundamental challenges in identification, inference, and…
As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set…
The paper concerns inference in the ill-conditioned functional response model, which is a part of functional data analysis. In this regression model, the functional response is modeled using several independent scalar variables. To verify…
The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
People employ the function-on-function regression to model the relationship between two random curves. Fitting this model, widely used strategies include algorithms falling into the framework of functional partial least squares (typically…
The estimation of cumulative distribution functions (CDF) is an important learning task with a great variety of downstream applications, such as risk assessments in predictions and decision making. In this paper, we study functional…
We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…
Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. Here we…