Related papers: A Robust Adaptive Modified Maximum Likelihood Esti…
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…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…
In this paper, we consider a linear regression model with AR(p) error terms with the assumption that the error terms have a t distribution as a heavy tailed alternative to the normal distribution. We obtain the estimators for the model…
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…
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…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
Bai (2010) and Bai et al. (2012) proposed robust mixture regression method based on the M regression estimation. However, the M-estimators are robust against the outliers in response variables, but they are not robust against the outliers…
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…
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…
Good robust estimators can be tuned to combine a high breakdown point and a specified asymptotic efficiency at a central model. This happens in regression with MM- and tau-estimators among others. However, the finite-sample efficiency of…
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…
Large outliers break down linear and nonlinear regression models. Robust regression methods allow one to filter out the outliers when building a model. By replacing the traditional least squares criterion with the least trimmed squares…
The bridge regression estimator generalizes both ridge regression and LASSO estimators. Since it minimizes the sum of squared residuals with a $L_{\gamma }$ penalty, this estimator is typically not robust against outliers in the data. There…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
While mixture of linear regressions (MLR) is a well-studied topic, prior works usually do not analyze such models for prediction error. In fact, {\em prediction} and {\em loss} are not well-defined in the context of mixtures. In this paper,…
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…
A robust estimator for a wide family of mixtures of linear regression is presented. Robustness is based on the joint adoption of the Cluster Weighted Model and of an estimator based on trimming and restrictions. The selected model provides…
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…