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Related papers: Linear Regression from 1-bit Quantized Data

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We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…

Machine Learning · Computer Science 2019-02-05 Max Simchowitz , Ross Boczar , Benjamin Recht

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Statistics Theory · Mathematics 2022-07-05 Yuliana Linke , Igor Borisov , Pavel Ruzankin , Vladimir Kutsenko , Elena Yarovaya , Svetlana Shalnova

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

Methodology · Statistics 2014-01-30 Stephen Reid , Robert Tibshirani , Jerome Friedman

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In…

Information Theory · Computer Science 2023-03-20 Arian Eamaz , Farhang Yeganegi , Deanna Needell , Mojtaba Soltanalian

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…

Statistics Theory · Mathematics 2021-10-07 Karine Bertin , Soledad Torres , Lauri Viitasaari

We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…

Methodology · Statistics 2026-02-05 Cheng Peng , Yizhou Li , Stan Uryasev

This paper studies inference for quadratic forms of linear regression coefficients with clustered data and many covariates. Our framework covers three important special cases: instrumental variables regression with many instruments and…

Econometrics · Economics 2026-02-18 Michal Kolesár , Pengjin Min , Wenjie Wang , Yichong Zhang

We consider the problem of robustly predicting as well as the best linear combination of $d$ given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For…

Statistics Theory · Mathematics 2012-02-24 Jean-Yves Audibert , Olivier Catoni

We analyze linear panel regression models with interactive fixed effects and predetermined regressors, for example lagged-dependent variables. The first-order asymptotic theory of the least squares (LS) estimator of the regression…

Econometrics · Economics 2026-05-04 Hyungsik Roger Moon , Martin Weidner

Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…

Methodology · Statistics 2018-04-10 German A. Schnaidt Grez , Brani Vidakovic

In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…

Machine Learning · Statistics 2022-06-08 Michał Dereziński , Manfred K. Warmuth , Daniel Hsu

Weak consistency and asymptotic normality of the ordinary least-squares estimator in a linear regression with adaptive learning is derived when the crucial, so-called, `gain' parameter is estimated in a first step by nonlinear least squares…

Econometrics · Economics 2023-01-11 Alexander Mayer

In this paper we study the least squares (LS) estimator in a linear panel regression model with unknown number of factors appearing as interactive fixed effects. Assuming that the number of factors used in estimation is larger than the true…

Econometrics · Economics 2026-05-04 Hyungsik Roger Moon , Martin Weidner

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

Statistics Theory · Mathematics 2021-10-01 Igor Silin , Jianqing Fan

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…

Statistics Theory · Mathematics 2015-03-13 Emilio Seijo , Bodhisattva Sen

We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…

Machine Learning · Statistics 2020-12-07 Ainesh Bakshi , Adarsh Prasad

In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…

Statistics Theory · Mathematics 2017-09-08 Bahadır Yüzbaşı , Yasin Asar , Ahmet Demiralp , M. Şamil Şık

Linear regression is a data analysis technique, which is categorized as supervised learning. By utilizing known data, we can predict unknown data. Recently, researchers have explored the use of quantum annealing (QA) to perform linear…

Quantum Physics · Physics 2024-10-14 Asuka Koura , Takashi Imoto , Katsuki Ura , Yuichiro Matsuzaki

We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…

Econometrics · Economics 2025-12-29 Takuya Ishihara , Masayuki Sawada , Kohei Yata

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

Methodology · Statistics 2019-09-09 Alexandre Belloni , Abhishek Kaul , Mathieu Rosenbaum