A thesis submitted in partial fulfilment of the requirement for the degree of Master of Engineering, School of Engineering and Technology

Thesis (M.Eng.) - Asian Institute of Technology, 1982

The present study investigates the estimation of regression parameters by minimizing mean of absolute deviation. Two LP formulations have been developed in this research, one for solving MINMAD regression with lesser number of variables and the other for solving the problem of best subset regression. Derivation of an analytical expression for distribution of parameters was tried and a rater complicated expression was found for the case of one independent variable, that is, for the case of simple linear regression. A set of simulation studies was carried out in this research in order to evaluate performances of MINMAD and LSM estimators both in presence of outliers in the data set and without them. MINMAD was found to perform much better than LSM in most of the cases. Further it was found that effect of outliers depend on their relative location in the data set. Also computational efficiency of certain specialized algorithms for solving MINMAD regression problem was tested by simulating data. An algorithm has been devised to solve a more general problem of regression by criterion of Minimizing Weighted Sum of Absolute Deviations using properties of optimal dual variables as well as by efficiently handling unrestricted variables in the simplex tableau. A computer code for the algorithm has been provided in the appendix. Another simulation study has been carried out to compare performances of the proposed algorithm with the algorithm developed by Narula and Wellington, by applying them to data set of different lengths and with different number of independent variables. It was found that the proposed performed better than that of Narula and Wellington with respect to computation time and provided better estimates. Finally, an extensive list of related literatures has been provided in the reference.