Sparsity identification for high-dimensional partially linear model with measurement error

References

• Brown, L. D., Levine, M., Wang, L. (2016). A semiparametric multivariate partially linear model: A difference approach. Journal of Statistical Planning and Inference 178:99–111.
   Google Scholar
• Buehlmann, P. (2006). Boosting for high-dimensional linear models. The Annals of Statistics 34(2):559–583.
   Google Scholar
• Carroll, R. J., Ruppert, D., Stefanski, L. A., Crainiceanu, C. M. (2010). Measurement Error in Nonlinear Models: A Modern Perspective. Boca Raton, FL: CRC Press.
   Google Scholar
• Chen, B., Yu, Y., Zou, H., Liang, H. (2012a). Profiled adaptive elastic-net procedure for partially linear models with high-dimensional covariates. Journal of Statistical Planning and Inference 142(7):1733–1745.
   Google Scholar
• Chen, J., Gao, J., Li, D. (2012b). Semiparametric trending panel data models with cross-sectional dependence. Journal of Econometrics 171(1):71–85.
   Google Scholar
• Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and it oracle properties. Journal of American Statistical Association 96(456):1348–1360.
   Google Scholar
• Fan, J., Peng, H. (2004). Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics 32(3):928–961.
   Google Scholar
• Fisher, C. K., Mehta, P. (2014). Fast Bayesian feature selection for high dimensional linear regression in genomics via the ising approximation. arXiv preprint arXiv:1407.8187.
   Google Scholar
• Gao, X., Ahmed, S. E. (2014). Efficient adaptive estimation strategies in high-dimensional partially linear regression models. Perspectives on Big Data Analysis: Methodologies and Applications 622:61–73.
   Google Scholar
• Huang, J., Horowitz, J. L., Ma, S. (2008a). Asymptotic properties of bridge estimators in sparse high-dimensional regression models. The Annals of Statistics 36(2):587–613.
   Google Scholar
• Huang, J., Ma, S., Zhang, C. H. (2008b). Adaptive Lasso for sparse high-dimensional regression models. Statistica Sinica 18(4):1603–1618.
   Google Scholar
• Liang, H., Härdle, W., Carroll, R. J. (1999). Estimation in a semiparametric partially linear errors-in-variables model. The Annals of Statistics 27(5):1519–1535.
   Google Scholar
• Liang, H., Li, R. (2009). Variable selection for partially linear models with measurement errors. Journal of the American Statistical Association 104(485):234–248.
   Google Scholar
• Li, G., Peng, H., Zhu, L. (2011). Nonconcave penalized M-estimation with a diverging number of parameters. Statistica Sinica 21(1):391–419.
   Google Scholar
• Luo, J., Gerard, P. (2013). Using thresholding difference-based estimators for variable selection in partial linear models. Statistics & Probability Letters 83(12):2601–2606.
   Google Scholar
• Munk, A., Bissantz, N., Wagner, T., Freitag, G. (2005). On difference based variance estimation in nonparametric regression when the covariate is high dimensional. Journal of Royal Statistical Society, Series B 67:19–41.
   Google Scholar
• Raskutti, G., Wainwright, M. J., Yu, B. (2011). Minimax rates of estimation for high-dimensional linear regression over-balls. IEEE Transactions on Information Theory 57(10):6976–6994.
   Google Scholar
• Subar, A. F., Thompson, F. E., Kipnis, V., Midthune, D., Hurwitz, P., McNutt, S., McIntosh, A., Rosenfeld, S. (2001). Comparative validation of the Block, Willett and National Cancer Institute food frequency questionnaires: The eating at America’s table study. American Journal of Epidemiology 154(12):1089–1099.
   Google Scholar
• Tabakan, G., Akdeniz, F. (2010). Difference-based ridge estimator of parameters in partial linear model. Statistical Papers 51(2):357–368.
   Google Scholar
• Wang, H. (2009). Forward regression for ultra-high dimensional variable screening. Journal of the American Statistical Association 104(488):1512–1524.
   Google Scholar
• Wang, H., Xia, Y. (2009). Shrinkage estimation of the varying coefficient model. Journal of the American Statistical Association 104(486):747–757.
   Google Scholar
• Wang, L., Brown, L. D., Cai, T. (2011). A difference based approach to the semiparametric partial linear model. Electronic Journal of Statistics 5:619–641.
   Google Scholar
• Wei, F., Huang, J. (2010). Consistent group selection in high-dimensional linear regression. Bernoulli 16(4):1369–1384.
   Google Scholar
• Wei, F., Huang, J., Li, H. (2011). Variable selection and estimation in high-dimensional varying-coefficient models. Statistica Sinica 21(4):1515–1540.
   Google Scholar
• Xie, H., Huang, J. (2009). SCAD-penalized regression in high-dimensional partially linear models. The Annals of Statistics 37(2):673–696.
   Google Scholar
• Yatchew, A. (1997). An elementary estimator of the partial linear model. Economics Letters 57(2):135–143.
   Google Scholar
• Yatchew, A. (2003). Semiparametric Regression for the Applied Econometrician. New York: Cambridge University Press.
   Google Scholar
• Zhang, C. H., Huang, J. (2008). The sparsity and bias of the Lasso selection in high-dimensional linear regression. The Annals of Statistics 36(4):1567–1594.
   Google Scholar
• Zou, H., Zhang, H. H. (2009). On the adaptive elastic-net with a diverging number of parameters. The Annals of Statistics 37(4):1733–1751.
   Google Scholar