A Maximum Likelihood Approach to Least Absolute Deviation Regression

A Maximum Likelihood Approach to Least Absolute Deviation Regression

Least absolute deviation (LAD) regression is an important tool used in numerous applications throughout science and engineering, mainly due to the intrinsic robust characteristics of LAD. In this paper, we show that the optimization needed to solve the LAD regression problem can be viewed as a sequence of maximum likelihood estimates (MLE) of location. The derived algorithm reduces to an iterat...

Analysis of least absolute deviation

The least absolute deviation or L1 method is a widely known alternative to the classical least squares or L2 method for statistical analysis of linear regression models. Instead of minimizing the sum of squared errors, it minimizes the sum of absolute values of errors. Despite its long history and many ground-breaking works (cf. Portnoy and Koenker (1997) and references therein), the former has...

Weighted Least Absolute Deviation Lasso Estimator

The linear absolute shrinkage and selection operator(Lasso) method improves the low prediction accuracy and poor interpretation of the ordinary least squares(OLS) estimate through the use of L1 regularization on the regression coefficients. However, the Lasso is not robust to outliers, because the Lasso method minimizes the sum of squared residual errors. Even though the least absolute deviatio...

Maximum Likelihood Regression Trees

We put forward a new method of growing regression trees via maximum likelihood. It inherits the CART (Brieman et al., 1984) backward fitting idea. However, standard likelihood based methods such as model selection criteria and likelihood ratio tests are naturally incorporated into each stage of the tree procedure. Compared with other least squared tree methods, maximum likelihood regression tre...

Least squares and maximum likelihood