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Penalized likelihood regression for generalized linear models with non-quadratic penalties

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  • Anestis Antoniadis
  • Irène Gijbels
  • Mila Nikolova

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  • 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.
    • Handle: RePEc:spr:aistmt:v:63:y:2011:i:3:p:585-615
    DOI: 10.1007/s10463-009-0242-4
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Yu Y. & Ruppert D., 2002. "Penalized Spline Estimation for Partially Linear Single-Index Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1042-1054, December.
    3. Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, March.
    4. D. G. T. Denison & B. K. Mallick & A. F. M. Smith, 1998. "Automatic Bayesian curve fitting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 333-350.
    5. Ming Yuan & Yi Lin, 2007. "On the non‐negative garrotte estimator," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 143-161, April.
    6. 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.
    7. Seiya Imoto & Sadanori Konishi, 2003. "Selection of smoothing parameters inB-spline nonparametric regression models using information criteria," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 671-687, December.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. V. K. Jandhyala & I. B. MacNeill, 1997. "Iterated Partial Sum Sequences of Regression Residuals and Tests for Changepoints with Continuity Constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 147-156.
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    Citations

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    Cited by:

    1. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    2. Y. Andriyana & I. Gijbels & A. Verhasselt, 2014. "P-splines quantile regression estimation in varying coefficient models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 153-194, March.
    3. Y. Andriyana & I. Gijbels & A. Verhasselt, 2018. "Quantile regression in varying-coefficient models: non-crossing quantile curves and heteroscedasticity," Statistical Papers, Springer, vol. 59(4), pages 1589-1621, December.
    4. Irène Gannaz, 2013. "Wavelet penalized likelihood estimation in generalized functional models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 122-158, March.
    5. Umberto Amato & Anestis Antoniadis & Italia Feis & Irène Gijbels, 2022. "Penalized wavelet estimation and robust denoising for irregular spaced data," Computational Statistics, Springer, vol. 37(4), pages 1621-1651, September.
    6. Shuichi Kawano, 2014. "Selection of tuning parameters in bridge regression models via Bayesian information criterion," Statistical Papers, Springer, vol. 55(4), pages 1207-1223, November.
    7. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(1), pages 187-207, February.
    8. Mandal, B.N. & Ma, Jun, 2016. "l1 regularized multiplicative iterative path algorithm for non-negative generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 289-299.
    9. Jason Xu & Eric C. Chi & Meng Yang & Kenneth Lange, 2018. "A majorization–minimization algorithm for split feasibility problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 795-828, December.

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