180
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

A Bayesian approach with generalized ridge estimation for high-dimensional regression and testing

&
Pages 6083-6105 | Received 28 Sep 2015, Accepted 19 May 2016, Published online: 21 Mar 2017

References

  • Allen, D. M. (1974). The relationship between variable selection and data augmentation and a method for prediction. Technometrics 16:125–127.
  • Araki, Y., Hattori, S. (2013). Efficient regularization parameter selection via information criteria. Communications in Statistics—Simulation and Computation 42(2):280–293.
  • Beer, D.G., Kardia, S.L.R., Huang, C.C., Giordano, T.J., Levin, A.M., et al. (2002). Gene-expression profiles predict survival of patients with lung adenocarcinoma. Nature Medicine 8:816–824.
  • Bühlmann, P. (2013). Statistical significance in high-dimensional linear models. Bernoulli 19:1212–1242.
  • Candes, E., Tao, T. (2007). The Dantzig selector: Statistical estimation when p is much larger than n. Annals of Statistics 35:2313–2351.
  • Chen, A. C., Emura, T. (2016). A modified Liu-type estimator with an intercept term under mixture experiments. Communications in Statistics-Theory and Method. DOI:10.1080/03610926.2015.1132327.
  • Chen, H.Y., Yu, S.L., Chen, C.H., Chang, G.C., Chen, C.Y., et al. (2007). A five-gene signature and clinical outcome in non-small-cell lung cancer. New England Journal of Medicine 356:11–20.
  • Cule, E., De Iorio, M. (2013). Ridge regression in prediction problems: Automatic choice of the ridge parameter. Genetic Epidemiology 37:704–714.
  • Cule, E., Vineis, P., De Iorio, M. (2011). Significance testing in ridge regression for genetic data. BMC Bioinformatrics 12:372.
  • Dicker, A. P., Rodeck, U. (2005). Predicting the future from trials of the past: Epidermal growth factor receptor expression and outcome of fractionated radiation therapy trials. Journal of Clinical Oncology 23:5437–5439.
  • Emura, T., Chen, Y. H. (2016). Gene selection for survival data under dependent censoring: a copula based approach. Statistical Methods in Medical Research 25(6):2840–2857.
  • Emura, T., Chen, H. Y., Chen, Y. H. (2017a). R compound.Cox: Estimation, Gene Selection, and Survival Prediction Based on the Compound Covariate Method Under the Cox Proportional Hazard Model, version 3.1, CRAN.
  • Emura, T., Chen, Y. H., Chen, H. Y. (2012). Survival prediction based on compound covariate under Cox proportional hazard models. PLoS ONE 7:e47627.
  • Emura, T., Nakatochi, M., Matsui, S., Michimae, H., Rondeau, V. (2017b). Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: Meta-analysis with a joint model, Statistical Methods in Medical Research. DOI:10.1177/0962280216688032.
  • Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96:1348–1360.
  • Fan, J., Lv, J. (2008). Sure independence screening for ultra-high dimensional feature space. (with discussion). Journal of Royal Statistical Society B 70:849–911.
  • Fan, T. H. (2001). Noninformative Bayesian estimation for the optimum in a single factor quadratic response model. Test 10(2):225–240.
  • Friedman, J., Hastie, T., Simon, N., Tibshirani, R. (2015). Glmnet: Lasso and Elastic-Net Regularized Generalized Linear Models, version 2.0–2. CRAN.
  • Golub, G. H., Heath, M., Wahba, G. (1979). Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21:215–223.
  • Hansen, B. E. (2016). The risk of James–Stein and Lasso shrinkage. Econometric Reviews 35(8-10):1456–1470.
  • Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning. New York: Springer-Verlag.
  • Hoerl, A. E., Kennard, R. W. (1970). Ridge regression: Biased estimation for nonorthogonal problems. Technometrics 12:55–67.
  • Jang, D.-H., Anderson-Cook, C. M. (2015). Visualization approaches for evaluating ridge regression estimators in mixture and mixture‐process experiments. Quality and Reliability Engineering International 31(8):1483–1494.
  • Jenssen, T.K., Kuo, W.P., Stokke, T., Hovig, E. (2002). Association between gene expressions in breast cancer and patient survival. Human Genetics 111:411–420.
  • Jimichi, M. (2008). Exact moments of feasible generalized ridge regression estimator and numerical evaluations. Journal of the Japanese Society of Computationl Statistics 21:1–20.
  • Kibria, B. M. G., Banik, S. (2016). Some ridge regression estimators and their performances. Journal of Modern Applied Statistical Methods 15(1):206–238.
  • Kim, S.-Y., Lee, J.-W. (2007). Ensemble clustering method based on the resampling similarity measure for gene expression data. Statistical Methods in Medical Research 16:539–564.
  • Loesgen, K.-H. (1990). A generalization and Bayesian interpretation of ridge-type estimators with good prior means. Statistical Papers 31:147–154.
  • Mallows, C. L. (1973). Some comments on Cp. Technometrics 15:661–675.
  • Matsui, S. (2006). Predicting survival outcomes using subsets of significant genes in prognostic marker studies with microarrays. BMC Bioinformatics 7:156.
  • Theobald, C. M. (1974). Generalizations of mean square error applied to ridge regression. Journal of the Royal Statistical Society B 36:103–106.
  • Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society B 58:267–288.
  • Trenkler, G. (1985). Mean square error matrix comparisons of estimators in linear regression. Communications in Statistics A 14:2495–2509.
  • Trenkler, G., Tourenburg, H. (1990). Mean squared error matrix comparisons between biased estimators – an overview of recent results. Statistical Papers 31:165–179.
  • Wain, J. M., Bruford, E. A., Lovering, R. C., et al. (2002). Guidelines for human gene nomenclature. Genomics 79:464–470.
  • Whittaker, J. C., Thompson, R., Denham, M. C. (2000). Marker-assisted selection using ridge regression. Genetical Research 75:249–252.
  • Wong, K. Y., Chiu, S. N. (2015). An iterative approach to minimize the mean squared error in ridge regression. Computational Statistics 30(2):625–639.
  • Yang, S. P. (2014). A class of generalized ridge estimator for high-dimensional linear regression. National Central University Electronic Theses & Dissertations. Taiwan, 1–41.
  • Zhang, C. H., Zhang, S. S. (2014). Confidence intervals for low dimensional parameters in high dimensional linear models. Journal of the Royal Statistical Society B 76(1):217–242.
  • Zhao, X., Rødland, E. A., Sørlie, T., et al. (2011). Combining gene signatures improves prediction of breast cancer survival. PLoS ONE 6:e17845.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.