Tuning Parameter Selection in Penalized Frailty Models

References

• Androulakis, E., Koukouvinos, C., Mylona, K., Vonta, F. (2010). A real survival analysis application via variable selection methods for Cox’s proportional hazards model. Journal of Applied Statistics 37:1399–1406.
   Web of Science ®Google Scholar
• Androulakis, E., Koukouvinos, C., Vonta, F. (2012). Estimation and variable selection via frailty models with penalized likelihood. Statistics in Medicine 31:2223–2239.
   PubMed Web of Science ®Google Scholar
• Androulakis, E., Koukouvinos, C., Vonta, F. (2014). Tuning parameter selection in penalized generalized linear models for discrete data. Statistica Neerlandica 68:276–292.
   Google Scholar
• Antoniadis, A. (1997). Wavelets in statistics: A review (with discussion). Journal of the Italian Statistical Society 6:97–144.
   Google Scholar
• Auchmuty, G. (1992). A posteriori error estimates for linear equations. Numerische Mathematik 61:1–6.
   Web of Science ®Google Scholar
• Bickel, P., Doksum, K. (2007). Mathematical Statistics, vol. I, 2nd ed. Upper Saddle River, New Jersey: Pearson Prentice Hall.
   Google Scholar
• Craven, P., Wahba, G. (1979). Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik 31:377–403.
   Web of Science ®Google Scholar
• Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Association 96:1348–1360.
   Web of Science ®Google Scholar
• Fan, J., Li, R. (2002). Variable selection for Cox’s proportional hazards model and frailty model. The Annals of Statistics 30:74–99.
   Web of Science ®Google Scholar
• Fan, J., Li, R. (2006). Statistical challenges with high dimensionality: Feature selection in knowledge discovery. In: Sanz-Sole, M., Soria, J., Varona, J.L., Verdera, J., eds. Proceedings of the International Congress of Mathematicians, Vol. 45. pp. 595–622.
   Google Scholar
• Fan, J., Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. Statistica Sinica 20:101–148.
   PubMed Web of Science ®Google Scholar
• Fan, Y., Tang, C. (2013). Tuning parameter selection in high dimensional penalized likelihood. Journal of the Royal Statistical Society: Series B 75:531–552.
   Google Scholar
• Galantai, A. (2001). A study of Auchmuty’s error estimate. Computers and Mathematics with Applications 42:1093–1102.
   Web of Science ®Google Scholar
• Greub, W., Rheinboldt, W. (1959). On a generalization of an inequality of L. V. Kantorovich. Proceedings of the American Mathematical Society 10:407–415.
   Google Scholar
• Horn, R.A., Johnson, C.R. (1985). Matrix Analysis. Cambridge: Cambridge University Press.
   Google Scholar
• Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York: Springer-Verlag.
   Google Scholar
• Kosorok, M., Lee, B., Fine, J. (2004). Robust inference for univariate proportional hazards frailty regression models. The Annals of Statistics 32:1448–1491.
   Web of Science ®Google Scholar
• Leng, C., Lin, Y., Wahba, G. (2006). A note on the LASSO and related procedures in model selection. Statistica Sinica 16:1273–1284.
   Web of Science ®Google Scholar
• Marcus, M., Minc, M. (1992). A Survey of Matrix Theory and Matrix Inequalities. New York: Dover.
   Google Scholar
• Nishii, R. (1984). Asymptotic properties of criteria for selection of variables in multiple regression. The Annals of Statistics 12:758–765.
   Web of Science ®Google Scholar
• Pötscher, B.M., Leeb, H. (2009). On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding. Journal of Multivariate Analysis 100:2065–2082.
   Web of Science ®Google Scholar
• The International Non-Hodgkin’s Lymphoma Prognostic Factors Project. (1993). A predictive model for aggressive non-Hodgkin’s lymphoma. The New England Journal Medicine 329:987–994.
   PubMed Web of Science ®Google Scholar
• Tibshirani, R.J. (1996). Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society: Series B 58:267–288.
   Google Scholar
• Van der Vaart, A. (1998). Asymptotic Statistics. Cambridge: Cambridge University Press.
   Google Scholar
• Wang, H., Li, R., Tsai, C.L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika 94:553–568.
   PubMed Web of Science ®Google Scholar
• Zhang, Y., Li, R., Tsai, C.-L. (2010). Regularization parameter selections via generalized information criterion. Journal of the American Statistical Association 105:312–323.
   PubMed Web of Science ®Google Scholar
• Zou, H., Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models. The Annals of Statistics 36:1509–1533.
   PubMed Web of Science ®Google Scholar