We treat bivariate nonparametric regression, where the design of experiment can be
arbitrarily irregular. Our method uses second-generation wavelets built with the lifting
scheme: Starting from a simple initial transform, we propose to use some predictor
operators based on a generalization in two dimensions of the Lagrange interpolating polynomial.
These predictors are meant to provide a smooth reconstruction. Next, we include
an update step which helps to reduce the correlation amongst the detail coecients, and
hence stabilizes the nal estimator. We use a Bayesian thresholding algorithm to denoise
the empirical coecients, and we show the performance of the resulting estimator through
a simulation study.
|Place of Publication
|Katholieke Universiteit Leuven
|Number of pages
|Published - 2003
|IAP Technical Report