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In this paper 1 we conducted a Monte Carlo investigation to reveal some characteristics of finite sample distributions of the Backfitting (B) and Marginal Integration (MI) estimators for an additive bivariate regression. We are particu larly interested in providing some evidence on how the different methods fo r the selection of bandwidth, such as the plug-in method, influence the finite sample properties of the MI and B estimators. We are also interested in providing evi dence on the behavior of different bandwidth estimators relatively to the optimal sequence that minimizes a chosen loss function. The impact of ignoring the de pendency between regressors is also investigated. Finally, differently from what occurs at the present time, when the B and MI estimators are used ad-hoc, our objective is to provide information that allows for a more accurate comparison of these two competing alternatives in a finite sample setting.