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Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing…

Machine Learning · Computer Science 2022-12-20 Andrew Stirn , Hans-Hermann Wessels , Megan Schertzer , Laura Pereira , Neville E. Sanjana , David A. Knowles

A linear multiple regression model in function spaces is formulated, under temporal correlated errors. This formulation involves kernel regressors. A generalized least-squared regression parameter estimator is derived. Its asymptotic…

Statistics Theory · Mathematics 2018-08-07 M. D. Ruiz-Medina , D. Miranda , R. M. Espejo

These notes aim at clarifying different strategies to perform linear regression from given dataset. Methods like the weighted and ordinary least squares, ridge regression or LASSO are proposed in the literature. The present article is my…

Methodology · Statistics 2019-08-12 Thierry A. Mara

Extensions of previous linear regression models for interval data are presented. A more flexible simple linear model is formalized. The new model may express cross-relationships between mid-points and spreads of the interval data in a…

Statistics Theory · Mathematics 2012-10-23 Angela Blanco-Fernández , Marta García-Bárzana , Ana Colubi , Erricos J. Kontoghiorghes

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

Methodology · Statistics 2023-06-22 Dan Ben-Moshe

It has been some time since interval-valued linear regression was investigated. In this paper, we focus on linear regression for interval-valued data within the framework of random sets. The model we propose generalizes a series of existing…

Methodology · Statistics 2015-06-12 Yan Sun , Chunyang Li

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

Statistics Theory · Mathematics 2009-06-18 Vladimir Vovk , Ilia Nouretdinov , Alex Gammerman

Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…

Statistics Theory · Mathematics 2016-05-17 Patrick Laurie Davies

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…

Statistics Theory · Mathematics 2018-04-10 Hisayuki Tsukuma

We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex…

Machine Learning · Computer Science 2023-04-03 Kaan Gokcesu , Hakan Gokcesu

We address the inference problem concerning regression coefficients in a classical linear regression model using least squares estimates. The analysis is conducted under circumstances where network dependency exists across units in the…

Methodology · Statistics 2024-04-03 Jing Lei , Kehui Chen , Haeun Moon

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Statistics Theory · Mathematics 2010-10-07 Yuao Hu

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

Methodology · Statistics 2025-07-08 Michael Lindon , Dae Woong Ham , Martin Tingley , Iavor Bojinov

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

In the last few decades both the volume of high-quality observing data on variable stars and common access to them have boomed; however the standard used methods of data processing and interpretation have lagged behind this progress. The…

Astrophysics · Physics 2007-11-29 Z. Mikulasek

Linear regression and classification methods with repeated functional data are considered. For each statistical unit in the sample, a real-valued parameter is observed over time under different conditions related by some neighborhood…

Methodology · Statistics 2024-09-23 Issam-Ali Moindjié , Cristian Preda , Sophie Dabo-Niang

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…

Econometrics · Economics 2025-12-10 Javier Alejo , Antonio F. Galvao , Julian Martinez-Iriarte , Gabriel Montes-Rojas

Traditionally, the least squares regression is mainly concerned with studying the effects of individual predictor variables, but strongly correlated variables generate multicollinearity which makes it difficult to study their effects.…

Methodology · Statistics 2022-12-22 Min Tsao

We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression…

Econometrics · Economics 2019-01-04 Richard Spady , Sami Stouli

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

Methodology · Statistics 2022-12-06 Yeonjoo Park , Kyunghee Han , Douglas G. Simpson