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In this paper, we study the properties of robust nonparametric estimation using deep neural networks for regression models with heavy tailed error distributions. We establish the non-asymptotic error bounds for a class of robust…
This study considers regression analysis of a circular response with an error-prone linear covariate. Starting with an existing estimator of the circular regression function that assumes error-free covariate, three approaches are proposed…
This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…
We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step…
In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…
Regression analysis is a standard supervised machine learning method used to model an outcome variable in terms of a set of predictor variables. In most real-world applications we do not know the true value of the outcome variable being…
In this paper, we consider the estimation of generalized linear models with covariates that are missing completely at random. We propose a model averaging estimation method and prove that the corresponding model averaging estimator is…
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,…
The standard quantile regression model assumes a linear relationship at the quantile of interest and that all variables are observed. We relax these assumptions by considering a partial linear model while allowing for missing linear…
Standard regression adjustment gives inconsistent estimates of causal effects when there are time-varying treatment effects and time-varying covariates. Loosely speaking, the issue is that some covariates are post-treatment variables…
In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator…
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…
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…
Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present…
This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…
This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven…