Related papers: On Measuring Model Complexity in Heteroscedastic L…
Multivariate linear regression models often face the problem of heteroscedasticity caused by multiple explanatory variables. The weighted least squares estimation with univariate-dependent weights has limitations in constructing weight…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…
The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…
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…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
Despite its prevalence in statistical datasets, heteroscedasticity (non-constant sample variances) has been largely ignored in the high-dimensional statistics literature. Recently, studies have shown that the Lasso can accommodate…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In…
The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…
The problem of detecting change points in the parameters of a linear regression model with errors and covariates exhibiting heteroscedasticity is considered. Asymptotic results for weighted functionals of the cumulative sum (CUSUM)…
The scope of this paper is the presentation of a test that enables to detect heteroscedasticity in univariate regression model. The test is simple to compute and very general since no hypothesis is made on the regularity of the response…
Overparametrized interpolating models have drawn increasing attention from machine learning. Some recent studies suggest that regularized interpolating models can generalize well. This phenomenon seemingly contradicts the conventional…
Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
Heteroskedastic errors can lead to inaccurate statistical conclusions if they are not properly handled. We introduce a test for heteroskedasticity for the nonparametric regression model with multiple covariates. It is based on a suitable…
Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…