Influence measure for the L1 regression

Because outliers and leverage observations unduly affect the least squares regression, the identification of influential observations is considered an important and integrai part of the analysis. However, very few techniques have been developed for the residual analysis and diagnostics for the minimum sum of absolute errors, L₁ regression. Although the L₁ regression is more resistant to the outliers than the least squares regression, it appears that outliers (leverage) in the predictor variables may affect it. In this paper, our objective is to develop an influence measure for the L₁ regression based on the likelihood displacement function. We illustrate the proposed influence measure with examples.     

An iterative procedure for the estimation of parameters in a dose-response model

The least squares estimates of the parameters in the multistage dose-response model are unduly affected by outliers in a data set whereas the minimum sum of absolute errors, MSAE estimates are more resistant to outliers. Algorithms to compute the MSAE estimates can be tedious and computationally burdensome. We propose a linear approximation for the dose-response model that can be used to find the MSAE estimates by a simple and computationally less intensive algorithm. A few illustrative ex-amples and a Monte Carlo study show that we get comparable values of the MSAE estimates of the parameters in a dose-response model using the exact model and the linear approximation.