Robust parameter estimation method for bilinear model

Abstract

This paper proposed the method of parameter estimation for bilinear model, especially on BL(1,0,1,1) model without and with the presence of additive outlier (AO). In this study, the estimated parameters for BL(1,0,1,1) model are using nonlinear least squares (LS) method and also through robust approaches. The LS method employs the Newton-Raphson (NR) iterative procedure in estimating the parameters of bilinear model, but, using LS in estimating the parameters can be affected with the occurrence of outliers. As a solution, this study proposed robust approaches in dealing with the problem of outliers specifically on AO in BL(1,0,1,1) model. In robust estimation method, for improvement, we proposed to modify the NR procedure with robust scale estimators. We introduced two robust scale estimators namely median absolute deviation (MADn) and Tn in linear autoregressive model, AR(1) that be adequate and suitable for bilinear BL(1,0,1,1) model. We used the estimated parameter value in AR(1) model as an initial value in estimating the parameter values of BL(1,0,1,1) model. The investigation of the performance of LS and robust estimation methods in estimating the coefficients of BL(1,0,1,1) model is carried out through simulation study. The achievement of performance for both methods will be assessed in terms of bias values. Numerical results present that, the robust estimation method performs better than LS method in estimating the parameters without and with the presence of AO.