Regression models for Boolean random sets

Abstract

In this paper we consider the regression problem for random sets of the Boolean-model type. Regression modeling of the Boolean random sets using some explanatory variables are classified according to the type of these variables as propagation, growth or propagation-growth models. The maximum likelihood estimation of the parameters for the propagation model is explained in detail for some specific link functions using three methods. These three methods of estimation are also compared in a simulation study.

Keywords:

• Random closed set
• Boolean model
• generalized linear model