Related papers: Estimation of functional derivatives
We study the problem of estimating a functional or a parameter in the context where outcome is subject to nonignorable missingness. We completely avoid modeling the regression relation, while allowing the propensity to be modeled by a…
Depth measures have gained popularity in the statistical literature for defining level sets in complex data structures like multivariate data, functional data, and graphs. Despite their versatility, integrating depth measures into…
This article introduces a non parametric warping model for functional data. When the outcome of an experiment is a sample of curves, data can be seen as realizations of a stochastic process, which takes into account the small variations…
We tackle estimation and prediction at non-visted sites in a spatial semi-functional linear regression model with derivatives that combines a functional linear model with a nonparametric regression one. The parametric part is estimated by a…
It is well known that eigenfunctions of a kernel play a crucial role in kernel regression. Through several examples, we demonstrate that even with the same set of eigenfunctions, the order of these functions significantly impacts regression…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
We propose a nonparametric additive model for estimating interpretable value functions in reinforcement learning, with an application in optimizing postoperative recovery through personalized, adaptive recommendations. While reinforcement…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
We propose a nonlinear function-on-function regression model where both the covariate and the response are random functions. The nonlinear regression is carried out in two steps: we first construct Hilbert spaces to accommodate the…
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood…
Standard regression approaches assume that some finite number of the response distribution characteristics, such as location and scale, change as a (parametric or nonparametric) function of predictors. However, it is not always appropriate…
The paper considers functional linear regression, where scalar responses $Y_1,\ldots,Y_n$ are modeled in dependence of i.i.d. random functions $X_1,\ldots,X_n$. We study a generalization of the classical functional linear regression model.…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
Regression models to relate a scalar $Y$ to a functional predictor $X(t)$ are becoming increasingly common. Work in this area has concentrated on estimating a coefficient function, $\beta(t)$, with $Y$ related to $X(t)$ through…
Measurement error is an important problem that has not been very well studied in the context of Functional Data Analysis. To the best of our knowledge, there are no existing methods that address the presence of functional measurement errors…
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 consider the problem of estimating an unknown function f* and its partial derivatives from a noisy data set of n observations, where we make no assumptions about f* except that it is smooth in the sense that it has square integrable…
We estimate the density and its derivatives using a local polynomial approximation to the logarithm of an unknown density $f$. The estimator is guaranteed to be nonnegative and achieves the same optimal rate of convergence in the interior…
Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling 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…