Related papers: Tilted Nonparametric Regression Function Estimatio…
We investigate nonparametric estimation of sliced inverse regression (SIR) via the $k$-nearest neighbors approach with a kernel. An estimator of the covariance matrix of the conditional expectation of the explanatory random vector given the…
This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro…
Data sampling is an effective method to improve the training speed of neural networks, with recent results demonstrating that it can even break the neural scaling laws. These results critically rely on high-quality scores to estimate the…
The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension…
We propose a new method for functional nonparametric regression with a predictor that resides on a finite-dimensional manifold but is only observable in an infinite-dimensional space. Contamination of the predictor due to discrete/noisy…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
The additive model is one of the most popular semiparametric models. The backfitting estimation (Buja, Hastie and Tibshirani, 1989, \textit{Ann. Statist.}) for the model is intuitively easy to understand and theoretically most efficient…
We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…
This paper is devoted to the nonparametric estimation of the derivative of the regression function in a nonparametric regression model. We implement a very efficient and easy to handle statistical procedure based on the derivative of the…
The nonparametric estimation of integrated diffusion processes has been extensively studied, with most existing research focusing on pointwise convergence. This paper is the first to establish uniform convergence rates for the…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between 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…
We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…
A key question in modern statistics is how to make fast and reliable inferences for complex, high-dimensional data. While there has been much interest in sparse techniques, current methods do not generalize well to data with nonlinear…
We consider nonparametric estimation of a regression function for a situation where precisely measured predictors are used to estimate the regression curve for coarsened, that is, less precise or contaminated predictors. Specifically, while…
In this paper, we investigate the adversarial robustness of nonparametric regression, a fundamental problem in machine learning, under the setting where an adversary can arbitrarily corrupt a subset of the input data. While the robustness…