Least absolute value regression: recent contributions

Understanding Least Absolute Value in Regression-based Data Mining

This article advances our understanding of regression-based data mining by comparing the utility of Least Absolute Value (LAV) and Least Squares (LS) regression methods. Using demographic variables from U.S. state-wide data, we fit variable regression models to dependent variables of varying distributions using both LS and LAV. Forecasts generated from the resulting equations are used to compar...

Least Absolute Value vs. Least Squares Estimation and Inference Procedures in Regression Models with Asymmetric Error Distributions

Empirical Regression Quantile

This study proposes a new use of goal programming for empirically estimating a regression quantile hyperplane. The approach can yield regression quantile estimates that are less sensitive to not only non-Gaussian error distribut.ions but also a small sample size t.han conventional regression quantile methods. The performance of regression quantile estimates is compared with least absolute value...

Solve least absolute value regression problems using modified goal programming techniques

Scope and PurposeÐLeast absolute value (LAV) regression methods have been widely applied in estimating regression equations. However, most of the current LAV methods are based on the original goal program developed over four decades. On the basis of a modi®ed goal program, this study reformulates the LAV problem using a markedly lower number of deviational variables than used in the current LAV...

Variable Selection in Nonparametric and Semiparametric Regression Models

This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD) or their variants, but restrict our attention to nonparametric a...