Strong consistency of the LAD (L/sub 1/) estimator of parameters of stationary autoregressive processes with zero mean

Strong consistency (almost sure convergence to the true parameters) of the LAD (least absolute deviations) AR (autoregressive) parameter estimator has been proven by S. Gross and W.L. Steiger (1979) under the condition that i.i.d. noise driving a stationary autoregressive process has zero median. This work extends their proof to include the case when the driving noise has zero mean. Thus, when the noise PDF (probability density function) is asymmetric with distinct mean and median, the LAD estimator will be strongly consistent with the PDF centered with either mean or median at the origin. The results of this work extend computer simulations which further indicate that under these conditions, the LAD estimator is MS consistent (mean-squared convergence to the true parameters). The importance of these results in LAD signal processing applications is discussed.<>