Inference in high dimensional generalized linear models based on soft thresholding

Artur Klinger

Journal of the Royal Statistical Society Series B, 2001, vol. 63, issue 2, 377-392

Abstract: We further develop and analyse penalized likelihood estimators for generalized linear models with a large number of coefficients. The methodology proposed leads to an adaptive selection of model terms without substantial variance inflation. Our proposal extends the soft thresholding strategy of Donoho and Johnstone and the lasso of Tibshirani to generalized linear models and multiple predictor variables. In addition, 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 methodology proposed 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 a prognosis of solvency and rental guides.

Date: 2001
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