Related papers: Efficient and Robust Estimation of Linear Regressi…
The panel data regression models have gained increasing attention in different areas of research including but not limited to econometrics, environmental sciences, epidemiology, behavioral and social sciences. However, the presence of…
In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…
This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…
This paper considers the problem of inference in a linear regression model with outliers where the number of outliers can grow with sample size but their proportion goes to 0. We apply the square-root lasso estimator penalizing the l1-norm…
The presence of outliers (anomalous values) in synthetic aperture radar (SAR) data and the misspecification in statistical image models may result in inaccurate inferences. To avoid such issues, the Rayleigh regression model based on a…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…
Linear regression estimators are known to be sensitive to outliers, and one alternative to obtain a robust and efficient estimator of the regression parameter is to model the error with Student's $t$ distribution. In this article, we…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
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…
Model averaging is an alternative to model selection for dealing with model uncertainty, which is widely used and very valuable. However, most of the existing model averaging methods are proposed based on the least squares loss function,…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…
This paper studies sparse linear regression analysis with outliers in the responses. A parameter vector for modeling outliers is added to the standard linear regression model and then the sparse estimation problem for both coefficients and…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
The aim of this paper is to present a new estimation procedure that can be applied in many statistical frameworks including density and regression and which leads to both robust and optimal (or nearly optimal) estimators. In density…
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…
Outliers widely occur in big-data applications and may severely affect statistical estimation and inference. In this paper, a framework of outlier-resistant estimation is introduced to robustify an arbitrarily given loss function. It has a…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…