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To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional…
A functional (lagged) time series regression model involves the regression of scalar response time series on a time series of regressors that consists of a sequence of random functions. In practice, the underlying regressor curve time…
This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown…
We consider a quadratic functional regression model in which a scalar response depends on a functional predictor; the common functional linear model is a special case. We wish to test the significance of the nonlinear term in the model. We…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
One of the challenges with functional data is incorporating spatial structure, or local correlation, into the analysis. This structure is inherent in the output from an increasing number of biomedical technologies, and a functional linear…
Subsampling is an efficient method to deal with massive data. In this paper, we investigate the optimal subsampling for linear quantile regression when the covariates are functions. The asymptotic distribution of the subsampling estimator…
In this study, we propose a function-on-function linear quantile regression model that allows for more than one functional predictor to establish a more flexible and robust approach. The proposed model is first transformed into a…
We propose a functional linear model to predict a response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g.…
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…
Frequency response function (FRF) estimation is a classical subject in system identification. In the past two decades, there have been remarkable advances in developing local methods for this subject, e.g., the local polynomial method,…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…