Generalized Soft-Thresholding and Varying-coefficient Models.
Collaborative Research Center 386, Discussion Paper 59
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.