Comparative Analysis of R-, M- and L-estimations of Regression Model Parameters

Student: Botvinkin Efim

Educational Programme: Data Science (Master)

Year of Graduation: 2016

In this paper a comparative analysis of several methods of regression parameter estimation is conducted. The list of techniques includes OLS, LAD, R-, M-, LMS-, LTS- and HBR-methods. The goal of this paper is to show advantages and disadvantages of each of these techniques of parameter estimation and to make some recommendations on applying one or another of methods. The comparison of the techniques is performed in terms of estimation accuracy on simulated regressions, asymptotic efficiencies of methods and breakdown points of estimations. There are used models with random and determined regressors and a wide range of noise distributions, including bimodal distributions and distributions with heavy tails. Asymptotic efficiencies are calculated for models with determined regressors. Results of comparison of estimations in terms of breakdown point are confirmed with an example on data with a cluster of outliers.

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