  Additive models and generalized additive models are effective semiparametric
tools for multidimensional data. In this article we propose an online smoothing
backfitting method for generalized additive models with local polynomial
smoothers. The main idea is to use a second order expansion to approximate the
nonlinear integral equations to maximize the local quasilikelihood and store
the coefficients as the sufficient statistics which can be updated in an online
manner by a dynamic candidate bandwidth method. The updating procedure only
depends on the stored sufficient statistics and the current data block. We
derive the asymptotic normality as well as the relative efficiency lower bounds
of the online estimates, which provides insight into the relationship between
estimation accuracy and computational cost driven by the length of candidate
bandwidth sequence. Simulations and real data examples are provided to validate
our findings.
