Bootstrap and backward elimination based approaches for model selection

This paper addresses the problem of model selection. Three different approaches for low order model selection are presented; a modified MDL/AIC based backward elimination approach, a modified F-statistic based backward elimination approach and a bootstrap-based approach. To compare the performances of these approaches, we apply each method to two different linear models; a moving average filter and a recursive filter. First we estimate the model parameters using least squares (LS) techniques in the time domain. Based on these estimates, a bootstrap-based multiple hypothesis test and two modified backward elimination based approaches are then applied to identify the true model, in other words the model corresponding to the true non-zero coefficients. Simulation results demonstrate the power of using each technique for model selection in a low SNR environment. A comparison between the proposed schemes are also presented.