On robust method of estimation in polynomial-sinusoidal regression

Abstract

In this paper we have considered the polynomial-sinusoidal regression model in presence of additive errors. The standard method of estimation of the unknown parameters is the least squares approach. It is well known that the least squares estimators are not robust in presence of outliers. We have proposed a weighted least squares method and it can be more robust than the least squares estimators in presence of outliers. The proposed weighted least squares method can be implemented very easily compared to some of the well known robust estimators like least absolute deviation estimators or Huber’s M (Huber-M) estimators. Theoretical properties of the proposed estimators have been obtained under the same set of assumptions as what are needed for the least squares estimators. Simulations have been performed to show the effectiveness of the proposed method, and it is observed that the weighted least squares estimators behave better than the least squares estimators in presence of outliers and they behave at par with the other robust estimators. Further, the implementation of the LAD and Huber-M estimators is computationally quite challenging when the number of components is large. It is observed that the performance of the weighted least squares estimators depends on the choice of the weight function. We have proposed a method to choose the proper weight function. We have analyzed one data set for illustrative purposes.