相关论文: Nonparametric Estimation of the Regression Functio…
The paper considers so-called adaptive estimations of regression, distribution density and spectral density of a Gaussian stationary sequence, asymptotically optimal in order at a growing number of observation on any regular subspace…
We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…
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…
Consider a regression model with infinitely many parameters and time series errors. We are interested in choosing weights for averaging across generalized least squares (GLS) estimators obtained from a set of approximating models. However,…
This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…
A least product relative error criterion is proposed for multiplicative regression models. It is invariant under scale transformation of the outcome and covariates. In addition, the objective function is smooth and convex, resulting in a…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…
We consider the problem of nonparametric estimation of a convex regression function $\phi_0$. We study the risk of the least squares estimator (LSE) under the natural squared error loss. We show that the risk is always bounded from above by…
Suppose the nonparametric regression function of a response variable $Y$ on covariates $X$ and $Z$ is an affine function of $X$ such that the slope $\beta$ and the intercept $\alpha$ are real valued measurable functions on the range of the…
This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a…
We develop nonparametric regression methods for the case when the true regression function is not necessarily smooth. More specifically, our approach is using the fractional Laplacian and is designed to handle the case when the true…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is…
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric…
We study a semi-/nonparametric regression model with a general form of nonclassical measurement error in the outcome variable. We show equivalence of this model to a generalized regression model. Our main identifying assumptions are a…
We discuss nonparametric estimation of the distribution function $G(x)$ of the autoregressive coefficient $a \in (-1,1)$ from a panel of $N$ random-coefficient AR(1) data, each of length $n$, by the empirical distribution function of lag 1…
This paper studies density estimation under pointwise loss in the setting of contamination model. The goal is to estimate $f(x_0)$ at some $x_0\in\mathbb{R}$ with i.i.d. observations, $$ X_1,\dots,X_n\sim (1-\epsilon)f+\epsilon g, $$ where…
We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…