A new approach of pole-zero modeling in the presence of white noise is proposed. While the model estimate is calculated through the conventional least square estimation, the choice of number of poles and zeros in this scenario is critical and a challenging task. A wrong choice can overfit the additive noise in larger orders or underfit and discard parts of the noiseless data in smaller orders. To overcome this issue, we choose the order through RE Minimization (REM). RE is the error between the observed noisy data and the unavailable noiseless output. Using the available output error, the method provides a probabilistic worst case upperbound for RE and optimizes it. Simulation results on generated synthetic data show advantages of REM compared to existing order selection methods such as AIC and BIC. The results show that the proposed method avoids over or under parametrizing of AIC and BIC. The results in a practical application of EOG artifacts removal of eye blinks from EEG data provides an efficient modeling of the true background EEG with optimal eye blink removal.