A Computationally Efficient Oracle Estimator for Additive Nonparametric Regression with Bootstrap Confidence Intervals
Woocheol Kim, Oliver B. Linton, Niklaus W. Hengartner · Journal of Computational and Graphical Statistics · 1999
This paper makes three contributions. First, we introduce a computationally efficient estimator for the component functions in additive nonparametric regression exploiting a different motivation from the marginal integration estimator of Linton and Nielsen (1995). Our method provides a reduction in computation of order n; which is highly significant in practice. Second, we define an efficient estimator of the additive components, by inserting the preliminary estimator into a backfitting algorithm but taking one step only, and establish that it is equivalent in various sense to the oracle estimator based on knowing the other components. Our two-step estimator is minimax superior to that considered in Opsomer and Ruppert (1997), due to its better bias. Third, we deøne a bootstrap algorithm for computing pointwise confidence intervals and show that it achieves the correct coverage.