In this article the family of polynomial estimators for the estimation of the linear system response of weakly non-linear systems is examined regarding estimation errors and applicability. The Ho estimator is introduced as an extension for measurement setups having both input and output noise and it is shown how the results obtained with the polynomial estimators are related to the parameters of Volterra models. The bias-variance tradeoff of the estimation error is derived and methods for obtaining the minimum error are presented.