To obtain certain estimators in statistical models, for example, M-estimators, it is often necessary to use an iterative computational technique. One such technique is the iterated weighted least squares method, while another is the well-known Newton1s method. Both methods require a starting value as well as a stopping rule incorporated into their iterative scheme. This paper attempts to indicate the possible effects of using various combinations of starting values and stopping rules on M-estimators, especially when applied to results of Monte Carlo studies. In this paper, H-estimators are computed for the first-order autoregressive model