To date the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct spe...

In this paper, we present a physics-based deformable model framework for the quantification of shape and motion parameters of the Left Anterior Descending (LAD) coronary artery in the heart’s local frame of reference. We define the long-axis of the heart as the local frame of reference. The shape of the LAD is modeled as a parametric curved axis with Frenet-Serret frame. The motion of the LAD (...

This report analyses the predictive performance of standard techniques for the ‘logical analysis of data’ (LAD), within a probabilistic framework. Improving and extending earlier results, we bound the generalization error of classifiers produced by standard LAD methods in terms of their complexity and how well they fit the training data. We also obtain bounds on the predictive accuracy which de...

Accurate effort prediction of software projects is of concern to portfolio managers, customers, vendors as well as project managers. Ordinary least squares (OLS) regression is widely used to create software prediction models, and it seems to perform just as well or better than most other, non-regression, prediction models. Software data sets may however exhibit certain characteristics that do n...

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...

The least absolute deviation (LAD) regression is a useful method for robust regression, and the least absolute shrinkage and selection operator (lasso) is a popular choice for shrinkage estimation and variable selection. In this article we combine these two classical ideas together to produce LAD-lasso. Compared with the LAD regression, LAD-lasso can do parameter estimation and variable selecti...

The Huber’s Criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. The adaptive weights in the adaptive lasso allow to have the oracle properties. In this paper we propose to combine the Huber’s criterion and adaptive penalty as lasso. This regression tech...

The least squares linear regression estimator is well-known to be highly sensitive to unusual observations in the data, and as a result many more robust estimators have been proposed as alternatives. One of the earliest proposals was least-sum of absolute deviations (LAD) regression, where the regression coefficients are estimated through minimization of the sum of the absolute values of the re...