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We advance both the theory and practice of robust $\ell_p$-quasinorm regression for $p \in (0,1]$ by using novel variants of iteratively reweighted least-squares (IRLS) to solve the underlying non-smooth problem. In the convex case, $p=1$,…

Optimization and Control · Mathematics 2022-10-14 Liangzu Peng , Christian Kümmerle , René Vidal

A function based nonlinear least squares estimation (FNLSE) method is proposed and investigated in parameter estimation of Jelinski-Moranda software reliability model. FNLSE extends the potential fitting functions of traditional least…

Methodology · Statistics 2011-08-29 Jingwei Liu , Meizhi Xu

The problem of fitting experimental data to a given model function $f(t; p_1,p_2,\dots,p_N)$ is conventionally solved numerically by methods such as that of Levenberg-Marquardt, which are based on approximating the Chi-squared measure of…

Optimization and Control · Mathematics 2017-03-14 Alberto Herrera-Gomez , R. Michael Porter

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Statistics Theory · Mathematics 2007-12-18 Jiming Jiang , Yihui Luan , You-Gan Wang

Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…

Machine Learning · Computer Science 2019-11-13 Yanyao Shen , Sujay Sanghavi

We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…

Statistics Theory · Mathematics 2022-02-25 Peijun Sang , Zuofeng Shang , Pang Du

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

Regression analysis is an important instrument to determine the effect of the explanatory variables on response variables. When outliers and bias errors are present, the standard weighted least squares estimator may perform poorly. For this…

Computation · Statistics 2025-02-11 Justo Puerto , Alberto Torrejon

Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…

Optimization and Control · Mathematics 2014-09-24 Necdet Serhat Aybat , Zi Wang

We propose a penalized least-squares method to fit the linear regression model with fitted values that are invariant to invertible linear transformations of the design matrix. This invariance is important, for example, when practitioners…

Methodology · Statistics 2024-10-11 Daeyoung Ham , Adam J. Rothman

In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…

Methodology · Statistics 2025-05-22 Minxuan Wu , Joseph Antonelli , Zhihua Su

In this paper, we give a tutorial on asymptotic properties of the Least Square (LS) and Regularized Least Squares (RLS) estimators for the finite impulse response model with filtered white noise inputs. We provide three perspectives: the…

Statistics Theory · Mathematics 2022-01-03 Yue Ju , Tianshi Chen , Biqiang Mu , Lennart Ljung

Functional data analysis is a fast evolving branch of modern statistics and the functional linear model has become popular in recent years. However, most estimation methods for this model rely on generalized least squares procedures and…

Methodology · Statistics 2020-06-24 Ioannis Kalogridis , Stefan Van Aelst

In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…

Methodology · Statistics 2020-07-01 Sukru Acitas , Peter Filzmoser , Birdal Senoglu

High-dimensional spectral data -- routinely generated in dairy production -- are used to predict a range of traits in milk products. Partial least squares (PLS) regression is ubiquitously used for these prediction tasks. However, PLS…

Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a…

Statistics Theory · Mathematics 2019-02-13 Markus Reiß , Martin Wahl

In this paper, we introduce a novel high-dimensional Factor-Adjusted sparse Partially Linear regression Model (FAPLM), to integrate the linear effects of high-dimensional latent factors with the nonparametric effects of low-dimensional…

Methodology · Statistics 2025-01-14 Yanmei Shi , Meiling Hao , Yanlin Tang , Xu Guo

We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional…

Statistics Theory · Mathematics 2017-12-27 Michael Levine

This paper proposes a new nonlinear approach for additive functional regression with functional response based on kernel methods along with some slight reformulation and implementation of the linear regression and the spectral additive…

This paper continues the research started in \cite{LW16}. In the framework of the convolution structure density model on $\bR^d$, we address the problem of adaptive minimax estimation with $\bL_p$--loss over the scale of anisotropic…

Statistics Theory · Mathematics 2017-04-17 Oleg Lepski , Thomas Willer