Abstract:

The least square method is popularly used in linear and non-linear regressions for data fitting and estimating model parameters. To improve the efficiency, a series of objective function are proposed and compared with the traditional objective function of least squares. By numerical tests, it is found that the objective function of summing up the deviation raised to 1.5 power shows in overall the best performance in retrieving the true functional relationship underlying the raw data superimposed with random Gaussian error.