Related papers: On a Projection Estimator of the Regression Functi…
We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
We consider the problem of estimating the joint distribution of $n$ independent random variables. Our approach is based on a family of candidate probabilities that we shall call a model and which is chosen to either contain the true…
The objective of this work is to propose an asymptotic correction method for the estimators of parameters from regression models with covariates subject to classification errors. A correction was developed based on the least squares…
We introduce a new family of estimators for unnormalized statistical models. Our family of estimators is parameterized by two nonlinear functions and uses a single sample from an auxiliary distribution, generalizing Maximum Likelihood Monte…
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…
This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
We consider inference on a scalar regression coefficient under a constraint on the magnitude of the control coefficients. A class of estimators based on a regularized propensity score regression is shown to exactly solve a tradeoff between…
We introduce and study a family of robust estimators for the functional logistic regression model whose robustness automatically adapts to the data thereby leading to estimators with high efficiency in clean data and a high degree of…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
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 study the properties of nonparametric least squares regression using deep neural networks. We derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer of feedforward deep neural regression. Our error…
Consider a nonlinear regression model : y_{i}=g(x_{i},{\theta})+e_{i}, i=1,...,n, where the x_{i} are random predictors x_{i} and {\theta} is the unknown parameter vector ranging in a set {\Theta}\subsetR^{p}. All known results on the…
In the context of nonparametric regression, we study conditions under which the consistency (and rates of convergence) of estimators built from discretely sampled curves can be derived from the consistency of estimators based on the…
Every observation may follow a distribution that is randomly selected in a class of distributions. It is called the distribution uncertainty. This is a fact acknowledged in some research fields such as financial risk measure. Thus, the…
Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo…
Many common estimators in machine learning and causal inference are linear smoothers, where the prediction is a weighted average of the training outcomes. Some estimators, such as ordinary least squares and kernel ridge regression, allow…