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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…

We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…

We consider the problem of causal structure learning in the setting of heterogeneous populations, i.e., populations in which a single causal structure does not adequately represent all population members, as is common in biological and…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Covariance function estimation is a fundamental task in multivariate functional data analysis and arises in many applications. In this paper, we consider estimating sparse covariance functions for high-dimensional functional data, where the…

In this paper, we are interested in the problem of smoothing parameter selection in nonparametric curve estimation under dependent errors. We focus on kernel estimation and the case when the errors form a general stationary sequence of…

Motivated by distinct walking patterns in real-world free-living gait data, this paper proposes an innovative curve-based sampling scheme for the analysis of functional data characterized by a mixture of covariance structures. Traditional…

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

We study kernel-based estimation of nonparametric time-varying parameters (TVPs) in linear models. Our contributions are threefold. First, we establish consistency and asymptotic normality of the kernel-based estimator for a broad class of…

We consider the problem of bandwidth selection by cross-validation from a sequential point of view in a nonparametric regression model. Having in mind that in applications one often aims at estimation, prediction and change detection…

Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…

In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…

Nonresponse frequently arises in practice, and simply ignoring it may lead to erroneous inference. Besides, the number of collected covariates may increase as the sample size in modern statistics, so parametric imputation or propensity…

The non-parametric estimation of average causal effects in observational studies often relies on controlling for confounding covariates through smoothing regression methods such as kernel, splines or local polynomial regression. Such…

Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…

We suggest two nonparametric approaches, based on kernel methods and orthogonal series to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems, we derive optimal convergence…