Related papers: Optimal Global Test for Functional Regression
We introduce two novel procedures to test the nullity of the slope function in the functional linear model with real output. The test statistics combine multiple testing ideas and random projections of the input data through functional…
Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…
The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…
This article studies global testing of the slope function in functional linear regression model in the framework of reproducing kernel Hilbert space. We propose a new testing statistic based on smoothness regularization estimators. The…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
We develop methodology for testing hypotheses regarding the slope function in functional linear regression for time series via a reproducing kernel Hilbert space approach. In contrast to most of the literature, which considers tests for the…
We investigate the problem of testing the global null in the high-dimensional regression models when the feature dimension $p$ grows proportionally to the number of observations $n$. Despite a number of prior work studying this problem,…
We develop dimension-reduction-free tests for the slope function in functional linear regression when the functional regressor may be endogenous or measured with error. The tests are based on a functional moment condition induced by an…
A goodness-of-fit test for the Functional Linear Model with Scalar Response (FLMSR) with responses Missing at Random (MAR) is proposed in this paper. The test statistic relies on a marked empirical process indexed by the projected…
In this work, a goodness-of-fit test for the null hypothesis of a functional linear model with scalar response is proposed. The test is based on a generalization to the functional framework of a previous one, designed for the…
We propose a novel method for testing the null hypothesis of no effect of a covariate on the response in the context of functional linear concurrent regression. We establish an equivalent random effects formulation of our functional…
We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$…
We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an…
In functional linear regression, the slope ``parameter'' is a function. Therefore, in a nonparametric context, it is determined by an infinite number of unknowns. Its estimation involves solving an ill-posed problem and has points of…
We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
The functional linear model is a popular tool to investigate the relationship between a scalar/functional response variable and a scalar/functional covariate. We generalize this model to a functional linear mixed-effects model when repeated…
Within the framework of smoothing spline ANOVA, we propose a plug-in kernel ridge regression estimator to estimate the derivatives of the underlying multivariate regression function. We first establish an $L_\infty$ convergence rate of the…
The generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable…
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…