English
Related papers

Related papers: Nonparametric, tuning-free estimation of S-shaped …

200 papers

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…

Methodology · Statistics 2011-06-08 P. A. Cornillon , N. Hengartner , E. Matzner-Løber

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…

Optimization and Control · Mathematics 2019-01-09 Paul Hand , Babhru Joshi

In this paper, we introduce a proximal-proximal majorization-minimization (PPMM) algorithm for nonconvex tuning-free robust regression problems. The basic idea is to apply the proximal majorization-minimization algorithm to solve the…

Optimization and Control · Mathematics 2021-06-28 Peipei Tang , Chengjing Wang , Bo Jiang

Convex regression is the problem of fitting a convex function to a data set consisting of input-output pairs. We present a new approach to this problem called spectrahedral regression, in which we fit a spectrahedral function to the data,…

Optimization and Control · Mathematics 2021-11-01 Eliza O'Reilly , Venkat Chandrasekaran

We consider the nonparametric regression estimation problem of recovering an unknown response function f on the basis of spatially inhomogeneous data when the design points follow a known compactly supported density g with a finite number…

Methodology · Statistics 2012-10-29 Anestis Antoniadis , Marianna Pensky , Theofanis Sapatinas

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…

Machine Learning · Statistics 2024-11-27 Masahiro Kato

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…

Statistics Theory · Mathematics 2008-12-18 Aurore Delaigle , Peter Hall , Hans-Georg Müller

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve first fitting non-parametric regression models…

Methodology · Statistics 2018-06-11 Guido Imbens , Stefan Wager

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…

Statistics Theory · Mathematics 2023-01-18 Yuling Jiao , Guohao Shen , Yuanyuan Lin , Jian Huang

We consider the problem of optimizing the sum of a smooth, nonconvex function for which derivatives are unavailable, and a convex, nonsmooth function with easy-to-evaluate proximal operator. Of particular focus is the case where the smooth…

Optimization and Control · Mathematics 2024-07-23 Yanjun Liu , Kevin H. Lam , Lindon Roberts

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Methodology · Statistics 2017-08-16 Dimitris Bertsimas , Martin S. Copenhaver , Rahul Mazumder

We study optimal procedures for estimating a linear functional based on observational data. In many problems of this kind, a widely used assumption is strict overlap, i.e., uniform boundedness of the importance ratio, which measures how…

Statistics Theory · Mathematics 2023-01-18 Wenlong Mou , Peng Ding , Martin J. Wainwright , Peter L. Bartlett

We consider a wavelet thresholding approach to adaptive variance function estimation in heteroscedastic nonparametric regression. A data-driven estimator is constructed by applying wavelet thresholding to the squared first-order differences…

Statistics Theory · Mathematics 2008-10-28 T. Tony Cai , Lie Wang

We consider the model of nonregular nonparametric regression where smoothness constraints are imposed on the regression function $f$ and the regression errors are assumed to decay with some sharpness level at their endpoints. The aim of…

Statistics Theory · Mathematics 2014-10-02 Moritz Jirak , Alexander Meister , Markus Reiß

We consider estimation and inference in a single index regression model with an unknown convex link function. We introduce a convex and Lipschitz constrained least squares estimator (CLSE) for both the parametric and the nonparametric…

Statistics Theory · Mathematics 2021-01-15 Arun K. Kuchibhotla , Rohit K. Patra , Bodhisattva Sen

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

Machine Learning · Computer Science 2019-05-28 Kwang-Sung Jun , Ashok Cutkosky , Francesco Orabona

Optimal estimation and inference for both the minimizer and minimum of a convex regression function under the white noise and nonparametric regression models are studied in a nonasymptotic local minimax framework, where the performance of a…

Statistics Theory · Mathematics 2024-03-12 T. Tony Cai , Ran Chen , Yuancheng Zhu

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…

Statistics Theory · Mathematics 2008-06-19 Ouerdia Arkoun , Serguei Pergamenchtchikov

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence…

Optimization and Control · Mathematics 2022-03-18 Matthew Hough , Lindon Roberts

In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…

Machine Learning · Statistics 2022-07-18 Junhong Lin , Alessandro Rudi , Lorenzo Rosasco , Volkan Cevher