Related papers: Nonparametric estimation in a regression model wit…
In this paper we develop a nonparametric regression method that is simultaneously adaptive over a wide range of function classes for the regression function and robust over a large collection of error distributions, including those that are…
We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…
Wavelet shrinkage estimators are widely applied in several fields of science for denoising data in wavelet domain by reducing the magnitudes of empirical coefficients. In nonparametric regression problem, most of the shrinkage rules are…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
We investigate the nonparametric bivariate additive regression estimation in the random design and long-memory errors and construct adaptive thresholding estimators based on wavelet series. The proposed approach achieves asymptotically…
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…
In a recent paper Birke and Bissantz (2008) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of…
Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive. In…
A $d$-dimensional nonparametric additive regression model with dependent observations is considered. Using the marginal integration technique and wavelets methodology, we develop a new adaptive estimator for a component of the additive…
This paper addresses the problem of regularity properties of functions represented as an expansion in a wavelet basis with random coefficients in terms of finiteness of their Besov norm with probability 1. Such representations are used to…
Estimation of a conditional mean (linking a set of features to an outcome of interest) is a fundamental statistical task. While there is an appeal to flexible nonparametric procedures, effective estimation in many classical nonparametric…
In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous…
Nonparametric density estimators are studied for $d$-dimensional, strongly spatial mixing data which is defined on a general $N$-dimensional lattice structure. We consider linear and nonlinear hard thresholded wavelet estimators which are…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…