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The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…
Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…
We propose a new variable selection procedure for a functional linear model with multiple scalar responses and multiple functional predictors. This method is based on basis expansions of the involved functional predictors and coefficients…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
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,…
Large health surveys increasingly collect high-dimensional functional data from wearable devices, and function on scalar regression (FoSR) is often used to quantify the relationship between these functional outcomes and scalar covariates…
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 consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
In this paper we investigate the problem of estimating the regression function in models with correlated observations. The data is obtained from several experimental units each of them forms a time series. We propose a new estimator based…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
In this paper, a functional partial quantile regression approach, a quantile regression analog of the functional partial least squares regression, is proposed to estimate the function-on-function linear quantile regression model. A partial…
Delineating the associations between images and a vector of covariates is of central interest in medical imaging studies. To tackle this problem of image response regression, we propose a novel nonparametric approach in the framework of…
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…
In this paper we introduce new estimators of the coefficient functions in the varying coefficient regression model. The proposed estimators are obtained by projecting the vector of the full-dimensional kernel-weighted local polynomial…
We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the…
This paper proposes distributed estimation procedures for three scalar-on-function regression models: the functional linear model (FLM), the functional non-parametric model (FNPM), and the functional partial linear model (FPLM). The…
We consider nonparametric prediction with multiple covariates, in particular categorical or functional predictors, or a mixture of both. The method proposed bases on an extension of the Nadaraya-Watson estimator where a kernel function is…
In the high-dimensional landscape, addressing the challenges of covariance regression with high-dimensional covariates has posed difficulties for conventional methodologies. This paper addresses these hurdles by presenting a novel approach…