In this thesis, we have given out a comprehensive approach to estimate the pairwise interaction in a bivariate additive model when the additive assumption is untenable. A new "nested backfilling' model fitting approach has been proposed and compared with some earlier approaches. The explicit estimators of each individual term were derived for the hierarchical bivariate additive model fitted by this "nested backfilling' approach. The convergence of the "nested backfilling" approach and the existence of these estimators have been shown depending on the ratio of the bandwidths that were used in the estimation of the effect of the same variable but in different terms. The mean average square error properties of these proposed explicit estimators were investigated. A discussion the pattern left in this bias and variance expressions derived for these estimators, such as mean corrected, Gauss-Seidel style etc., were provided to facilitate the understanding these properties. Unlike in the pure additive model case, the mean average square error of our model cannot be attributed to each individual variable. The four optimal bandwidths used need to be selected simultaneously to minimize the mean average square error. These estimators were shown worked reasonably well in simulated datasets, regardless of the level of dependence of the covariates.