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Inference in high dimensional generalized linear models based on soft thresholding

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  • Artur Klinger

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.

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  • Artur Klinger, 2001. "Inference in high dimensional generalized linear models based on soft thresholding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 377-392.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:2:p:377-392
    DOI: 10.1111/1467-9868.00291
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    Cited by:

    1. Román Salmerón Gómez & Ainara Rodríguez Sánchez & Catalina García García & José García Pérez, 2020. "The VIF and MSE in Raise Regression," Mathematics, MDPI, vol. 8(4), pages 1-28, April.
    2. Anestis Antoniadis & Irène Gijbels & Mila Nikolova, 2011. "Penalized likelihood regression for generalized linear models with non-quadratic penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 585-615, June.
    3. Tutz, Gerhard & Leitenstorfer, Florian, 2006. "Response shrinkage estimators in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2878-2901, June.
    4. Lansangan, Joseph Ryan G. & Barrios, Erniel B., 2017. "Simultaneous dimension reduction and variable selection in modeling high dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 242-256.
    5. Chang, Xiao-Wen & Qu, Leming, 2004. "Wavelet estimation of partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 31-48, August.

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