New algorithm of Location Model based on robust estimators and smoothing approach

Abstract

Location Model is a classification model that capable to deal with mixtures of binary and continuous variables simultaneously. The binary variables create segmentation in the groups called cells whilst the continuous variables measure the differences between groups based on information inside the cells. It is important to note that location model is biased and even impossible to be constructed when involving some empty cells. Interestingly from previous studies, smoothing approach managed to remedy the effects of some empty cells. However, numerical analysis has demonstrated that the performances of the location model based on smoothing approach are good in most situations except if there are outliers in the sample. Thus, the presence of outliers has alarmed us to do further investigation towards the performance of the location model. Instead of transformations or truncation, many researchers used various robust procedures to protect their data from being distorted by outliers. Therefore, in this paper, we develop a new methodology of the location model through new estimators resulting from an integration of robust estimators and smoothing approach to address both issues of outliers and empty cells simultaneously. It is expected that this new methodology will offer another potential tool to practitioners, which is possible to be considered in classification problems when the data samples contain outliers and at the same time could resolve the crisis of some empty cells of the location model.