  This paper introduces an interpolation-based method, called the
reconstruction approach, for nonparametric regression. Based on the fact that
interpolation usually has negligible errors compared to statistical estimation,
the reconstruction approach uses an interpolator to parameterize the regression
function with its values at finite knots, and then estimates these values by
(regularized) least squares. Some popular methods including kernel ridge
regression can be viewed as its special cases. It is shown that, the
reconstruction idea not only provides different angles to look into existing
methods, but also produces new effective experimental design and estimation
methods for nonparametric models. In particular, for some methods of complexity
O(n3), where n is the sample size, this approach provides effective surrogates
with much less computational burden. This point makes it very suitable for
large datasets.
