English
Related papers

Related papers: Equivariant adjusted least squares estimator in tw…

200 papers

Protesting mildly against the notion of an exactly correct parametric model the view is adopted that the logistic regression equation is merely an approximation to the underlying, true function. The behaviour of likelihood based estimators…

Statistics Theory · Mathematics 2026-05-27 Nils Lid Hjort

In the linear random effects model, when distributional assumptions such as normality of the error variables cannot be justified, moments may serve as alternatives to describe relevant distributions in neighborhoods of their means.…

Statistics Theory · Mathematics 2012-03-05 Ping Wu , Winfried Stute , Li-Xing Zhu

We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…

Statistics Theory · Mathematics 2017-10-09 Olivier Collier , Laëtitia Comminges , Alexandre B. Tsybakov , Nicolas Verzélen

The a posteriori error estimator using the least-squares functional can be used for adaptive mesh refinement and error control even if the numerical approximations are not obtained from the corresponding least-squares method. This suggests…

Numerical Analysis · Mathematics 2024-07-19 Ziyan Li , Shun Zhang

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

Statistics Theory · Mathematics 2025-06-03 Yannick Baraud , Guillaume Maillard

The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…

Optimization and Control · Mathematics 2021-10-13 Alberto Padoan

In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…

Statistics Theory · Mathematics 2007-06-13 Ana K. Fermin , Carenne Ludena

In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…

Machine Learning · Statistics 2016-08-11 Aditi Raghunathan , Roy Frostig , John Duchi , Percy Liang

We propose a novel estimation approach for a general class of semi-parametric time series models where the conditional expectation is modeled through a parametric function. The proposed class of estimators is based on a Gaussian…

Methodology · Statistics 2025-07-21 Mirko Armillotta , Paolo Gorgi

General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the…

Statistics Theory · Mathematics 2025-03-11 Hirai Mukasa , Koji Tsukuda

In this article, we study the performance of the estimator that minimizes $L_{2k}- $ order loss function (for $ k \ge \; 2 )$ against the estimators which minimizes the $L_2-$ order loss function (or the least squares estimator). Commonly…

Statistics Theory · Mathematics 2019-03-20 Gopal K Basak , Samarjit Das , Arijit De , Atanu Biswas

We study quasilinear elliptic double obstacle problems with a variable exponent growth when the right-hand side is a measure. A global Calder\'{o}n-Zygmund estimate for the gradient of an approximable solution is obtained in terms of the…

Analysis of PDEs · Mathematics 2021-05-25 Sun-Sig Byun , Yumi Cho , Jung-Tae Park

The field of machine have seen rising applications of equivariance criterion. However, there is no systematic way to justify its usage, including why it works, whether there is an optimal solution and if so, what form it carries. In this…

Statistics Theory · Mathematics 2025-09-23 Daowei Wang , Mian Wu , Haojin Zhou

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…

Statistics Theory · Mathematics 2016-02-12 Holger Dette , Andrey Pepelyshev , Anatoly Zhigljavsky

Adequacy for estimation between an inferential method and a model can be de{\ldots}ned through two main requirements: {\ldots}rstly the inferential tool should de{\ldots}ne a well posed problem when applied to the model; secondly the…

Statistics Theory · Mathematics 2025-07-30 Michel Broniatowski , Justin Moutsouka

This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…

Statistics Theory · Mathematics 2008-02-20 Joseph Rynkiewicz

Estimation of the parameters of a 2-dimensional sinusoidal model is a fundamental problem in digital signal processing and time series analysis. In this paper, we propose a robust least absolute deviation (LAD) estimators for parameter…

Statistics Theory · Mathematics 2023-06-19 Saptarshi Roy , Amit Mitra , N K Archak

We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…

Statistics Theory · Mathematics 2021-04-12 Arun K. Kuchibhotla , Rohit K. Patra

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

Statistics Theory · Mathematics 2012-06-06 Jun Shao , Xinwei Deng

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…

Methodology · Statistics 2025-07-11 Alexandre Garcia Dias , Mariana Rodrigues Motta , Alexandre Hild Aono