Inference in High Dimensional Generalized Linear Models based on Soft-Thresholding.
Collaborative Research Center 386, Discussion Paper 165
We propose a new method for estimation of a high number of coefficients within the generalized linear model framework. The estimator leads to an adaptive selection of model terms without substantial variance inflation. Our proposal extends the soft-thresholding strategy from Donoho and Johnstone (1994) to generalized linear models and multiple predictor variables. Furthermore, we develop an estimator for the covariance matrix of the estimated coefficients, which can even be used for terms dropped from the model. Used in connection with basis functions, the proposed methodology provides an alternative to other generalized function estimators. It leads to an adaptive economical description of the results in terms of basis functions. Specifically, it is shown how adaptive regression splines and qualitative restrictions can be incorporated. Our approach is demonstrated by applications to solvency prognosis and rental guides.