On RA and GM Estimates for Spatial Autoregressive Models

This paper is concerned with the computational implementation of the robust RA estimates for spatial autoregressive (AR-2D) models with three parameters. The computational behavior of the RA estimators for AR-2D models which depends on the number of parameters in the model, has been studied for those models containing at most two parameters. A simulation study is carried out to compare the relative performance of GM and RA estimators under additive contamination, and to compare the RA and GM estimators with the M and LS estimators. This implementation can be explored in models with more than three parameters. Keywords: AR-2D model, RA and GM estimators, Additive Outlier. 1 Introduction and Motivation Most of the real images of interest, e.g. the images of cultivated …elds and concentration of population are naturally rich in texture, level of gray, etc.. The same thing happens to the images of geographical regions that allows the making of maps and, in general, almost all the images of the earth. In this sense the AR-2D model is an adequate model to show the diversity of the real sceneries. Another desirable feature of a model for images is parsimony, which is, the capability to represent different real sceneries without requiring a large number of parameters. To illustrate the capability of this model, in Figure 1 we show four images generated from AR-2D models with di¤erent sets of parameters. Corresponding author: Departamento de Estadística, Universidad de Valparaíso, Avenida Gran Bretaña 1091, Playa Ancha, Valparaíso, Chile. E-mail: [email protected]