Bayesian estimation and variables selection for binary composite quantile regression

In this paper, Bayesian hierarchical model proposed to estimate the coefficients of the composite quantile regression model when the response variable is binary. For selecting variables in binary composite quantile regression lasso the adaptive lasso penalty is derived in a Bayesian framework. Simulation study and real data examples are used to examine the performance of the proposed methods compared to the other existing methods. We conclude that the proposed method is comparable

Sparsity via new Bayesian Lasso

Lasso estimate as the posterior mode assuming that the parameter has prior density as double exponential distribution [1]. In this paper, we proposed Scale Mixture of Normals mixing with Rayleigh (SMNR) density on their variances to represent the double exponential distribution. Hierarchical model formulation presented with Gibbs sampler under SMNR as alternative Bayesian analysis of minimization problem of classical lasso. We conducted two simulation examples to explore path solution of the Ridge, Lasso, Bayesian Lasso, and New Bayesian Lasso (R, L, BL, NBL) regression methods through the prediction accuracy using the bias of the estimates with different sample sizes, bias indicates that the lasso regression perform well, followed by the NBL. The Median Mean Absolute Deviations (MMAD) used to compared the perform of the regression methods using real data, MMAD indicates that the proposed method (NBL) perform better than the others

Bayesian extensions on Lasso and adaptive Lasso Tobit regressions

Since lasso method launched, a lot of applications and extensions were run on it which made it to become deeply widely used in various discipline. In this paper, we proposed the Scale Mixture of Normals mixing with Rayleigh (SMNR) distribution on their variances to represent the double exponential distribution. Hierarchical model formula have derived with Gibbs sampler for SMNR. The proposed models; Bayesian Tobit Adaptive Lasso (BTAL) and Bayesian Tobit Lasso (BTL) models are illustrated using simulation example and a real data example through the prediction accuracy using the estimated relative efficiency with different sample. This is the first work that discussed regularization regression models under SMNR

Elastic net for single index support vector regression model

The single index model (SIM) is a useful regression tool used to alleviate the so-called curse of dimensionality. In this paper, we propose a variable selection technique for the SIM by combining the estimation method with the Elastic Net penalized method to get sparse estimation of the index parameters. Furthermore, we propose the support vector regression (SVR) to estimate the unknown nonparametric link function due to its ability to fit the non-linear relationships and the high dimensional problems. This make the proposed work is not only for estimating the parameters and the unknown link function of the single index model, but also for selecting the important variables simultaneously. Simulations of various single index models with nonlinear relationships among variables are conducted to demonstrate the effectiveness of the proposed semi-parametric estimation and the variable selection versus the existing fully parametric SVR method. Moreover, the proposed method is illustrated by analyzing a real data set. A data analysis is given which highlights the utility of the suggested methodology

Modified Least Trimmed Quantile Regression to Overcome Effects of Leverage Points

Quantile regression estimates are robust for outliers in y direction but are sensitive to leverage points. The least trimmed quantile regression (LTQReg) method is put forward to overcome the effect of leverage points. The LTQReg method trims higher residuals based on trimming percentage specified by the data. However, leverage points do not always produce high residuals, and hence, the trimming percentage should be specified based on the ratio of contamination, not determined by a researcher. In this paper, we propose a modified least trimmed quantile regression method based on reweighted least trimmed squares. Robust Mahalanobis’ distance and GM6 weights based on Gervini and Yohai’s (2003) cutoff points are employed to determine the trimming percentage and to detect leverage points. A simulation study and real data are considered to investigate the performance of our proposed methods