Generalized Soft-Thresholding and Varying-coefficient Models

We propose a new method for estimation of unknown functions within
the generalized linear model framework. The estimator leads to an
adaptive economical description of the results in terms of basis
functions. Our proposal extends the soft--thresholding strategy
from ordinary wavelet regression to generalized linear models and
multiple predictor variables. Several sets of basis functions,
tailored to specific purposes, can be incorporated into our
methodology. We discuss semiparametric statistical inference based
on generalized soft--thresholding. An algorithm which produces a
sequence of estimates corresponding to increasing model complexity
is developed. Advantages of our approach are demonstrated by an
application to German labour market data.