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Inference in high dimensional generalized linear models based on soft thresholding
Author(s) -
Klinger Artur
Publication year - 2001
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00291
Subject(s) - estimator , mathematics , generalized linear model , linear model , model selection , mathematical optimization , lasso (programming language) , basis (linear algebra) , linear regression , computer science , statistics , geometry , world wide web
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.