Related papers: Adaptive variance function estimation in heterosce…
Given any domain $X\subseteq \mathbb{R}^d$ and a probability measure $\rho$ on $X$, we study the problem of approximating in $L^2(X,\rho)$ a given function $u:X\to\mathbb{R}$, using its noiseless pointwise evaluations at random samples. For…
This paper introduces a data-adaptive non-parametric approach for the estimation of time-varying spectral densities from nonstationary time series. Time-varying spectral densities are commonly estimated by local kernel smoothing. The…
There has been substantial recent work on methods for estimating the slope function in linear regression for functional data analysis. However, as in the case of more conventional finite-dimensional regression, much of the practical…
The paper deals with asymptotic properties of the adaptive procedure proposed in the author paper, 2007, for estimating an unknown nonparametric regression. %\cite{GaPe1}. We prove that this procedure is asymptotically efficient for a…
We introduce a robust and fully adaptive method for pointwise estimation in heteroscedastic regression. We allow for noise and design distributions that are unknown and fulfill very weak assumptions only. In particular, we do not impose…
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…
Consider the case that we observe $n$ independent and identically distributed copies of a random variable with a probability distribution known to be an element of a specified statistical model. We are interested in estimating an infinite…
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…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
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…
In this paper we consider a heteroscedastic transformation model, where the transformation belongs to a parametric family of monotone transformations, the regression and variance function are modelled nonparametrically and the error is…
The adaptive non-harmonic (ANH) model is a powerful tool to compactly represent oscillating signals with time-varying amplitude and phase, and non-sinusoidal oscillating morphology. Given good estimators of instantaneous amplitude and phase…
This paper concerns the estimation of the regression function at a given point in nonparametric heteroscedastic models with Gaussian noise or with noise having unknown distribution. In the two cases an asymptotically efficient kernel…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…
Despite tremendous advancements of machine learning models and algorithms in various application domains, they are known to be vulnerable to subtle, natural or intentionally crafted perturbations in future input data, known as adversarial…
This paper is concerned with a semiparametric partially linear regression model with unknown regression coefficients, an unknown nonparametric function for the non-linear component, and unobservable Gaussian distributed random errors. We…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…
Estimation of large covariance matrices has drawn considerable recent attention, and the theoretical focus so far has mainly been on developing a minimax theory over a fixed parameter space. In this paper, we consider adaptive covariance…
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…