  This paper is concerned with asymptotic theory for penalized spline estimator
in bivariate additive model. The focus of this paper is put upon the penalized
spline estimator obtained by the backfitting algorithm. The convergence of the
algorithm as well as the uniqueness of its solution are shown. The asymptotic
bias and variance of penalized spline estimator are derived by an efficient use
of the asymptotic results for the penalized spline estimator in marginal
univariate model. Asymptotic normality of estimator is also developed, by which
an approximate confidence interval can be obtained. Some numerical experiments
confirming theoretical results are provided.
