Ultrahigh-dimensional sufficient dimension reduction for censored data with measurement error in covariates

References

• J. Buckley and I. James, Linear regression with censored data, Biometrika 66 (1979), pp. 429–436.
   Web of Science ®Google Scholar
• R.J. Carroll and K.-C. Li, Measurement error regression witht unknown link: Dimension reduction and data visualization, J. Am. Stat. Assoc. 87 (1992), pp. 1040–1050.
   Web of Science ®Google Scholar
• R.J. Carroll, D. Ruppert, L.A. Stefanski, and C.M. Crainiceanu, Measurement Error in Nonlinear Model, CRC Press, New York, 2006.
   Google Scholar
• X. Chen, X. Chen, and H. Wang, Robust feature screening for ultra-high dimensional right censored data via distance correlation, Comput. Statist. Data Anal. 119 (2018), pp. 118–138.
   Web of Science ®Google Scholar
• X. Chen, Y. Zhang, X. Chen, and Y. Liu, A simple model-free survival conditional feature screening, Statist. Probab. Lett. 146 (2019), pp. 156–160.
   Web of Science ®Google Scholar
• R.D. Cook, On the interpretation of regression plots, J. Am. Stat. Assoc. 89 (1994), pp. 177–189.
   Web of Science ®Google Scholar
• R.D. Cook, Regression Graphics: Ideas for Studying Regressions Through Graphics, Wiley, New York, 1998.
   Google Scholar
• S. Ding, W. Qian, and L Wang, Double-slicing assisted sufficient dimension reduction for high dimensional censored data, Ann. Statist. 48 (2020), pp. 2132–2154.
   Web of Science ®Google Scholar
• J. Fan and J. Lv, Sure independence screening for ultra-high dimensional feature space, J. R. Stat. Soc. Ser. B 70 (2008), pp. 849–911.
   PubMed Web of Science ®Google Scholar
• M.-Y. Huang and K.C.G Chan, Sufficient dimension reduction with simultaneous estimation of effective dimensions for time-to-event data, Stat. Sin. (2019). doi:https://doi.org/10.5705/ss.202017.0550.
   Google Scholar
• B. Li, Sufficient Dimension Reduction: Methods and Applications with R, CRC Press, New York, 2018.
   Google Scholar
• B. Li and S. Wang, On directional regression for dimension reduction, J. Am. Stat. Assoc. 102 (2007), pp. 997–1008.
   Web of Science ®Google Scholar
• B. Li and X. Yin, On surrogate dimension reduction for measurement error regression: An invariance law, Ann. Statist. 35 (2007), pp. 2143–2172.
   Web of Science ®Google Scholar
• K.-C. Li, Sliced inverse regression for dimension reduction, J. Am. Stat. Assoc. 86 (1991), pp. 316–327.
   Web of Science ®Google Scholar
• K.-C. Li, J.-L. Wang, and C.-H. Chen, Dimension reduction for censored regression data, Ann. Statist. 27 (1999), pp. 1–23.
   Web of Science ®Google Scholar
• R. Li, W. Zhong, and L. Zhu, Feature screening via distance correlation learning, J. Am. Stat. Assoc. 107 (2012), pp. 1129–1139.
   PubMed Web of Science ®Google Scholar
• W. Lu and L. Li, Sufficient dimension reduction for censored regression, Biometrics 67 (2011), pp. 513–523.
   PubMed Web of Science ®Google Scholar
• H.-H. Lue, Principal Hessian directions for regression with measurement error, Biometrika 91 (2004), pp. 409–423.
   Web of Science ®Google Scholar
• H.-H. Lue, C.-H. Chen, and W.-H. Chang, Dimension reduction in survival regressions with censored data via an imputed spline approach, Biom. J. 53 (2011), pp. 426–443.
   PubMed Web of Science ®Google Scholar
• Y. Ma and L. Zhu, A semiparametric approach to dimension reduction, J. Am. Stat. Assoc. 107 (2012), pp. 168–179.
   PubMed Web of Science ®Google Scholar
• Y. Ma and L. Zhu, Efficient estimation in sufficient dimension reduction, Ann. Statist. 41 (2013), pp. 250–268.
   PubMed Web of Science ®Google Scholar
• R.G. Miller, Survival Analysis, Wiley, New York, 1981.
   Google Scholar
• N.V. Nadkarni, Y. Zhao, and M.R. Kosorok, Inverse regression estimation for censored data, J. Am. Stat. Assoc. 106 (2011), pp. 178–190.
   PubMed Web of Science ®Google Scholar
• W. Qian, S. Ding, and R.D. Cook, Sparse minimum discrepancy approach to sufficient dimension reduction with simultaneous variable selection in ultrahigh dimension, J. Am. Stat. Assoc. 114 (2019), pp. 1277–1290.
   Web of Science ®Google Scholar
• D.M. Rocke and B. Durbin, A model for measurement error for gene expression arrays, J. Comput. Biol. 8 (2001), pp. 557–569.
   PubMed Web of Science ®Google Scholar
• R. Song, W. Lu, S. Ma, and X.J. Jeng, Censored rank independence screening for high-dimensional survival data, Biometrika 101 (2014), pp. 799–814.
   PubMed Web of Science ®Google Scholar
• V. Susarla, W.Y. Tsai, and J.V. Ryzin, A Buckley-James-type estimator for the mean with censored data, Biometrika 71 (1984), pp. 624–625.
   Web of Science ®Google Scholar
• G.J. Székely, M.L. Rizzo, and N.K. Bakirov, Measuring and testing dependence by correlation of distances, Ann. Statist. 35 (2007), pp. 2769–2794.
   Web of Science ®Google Scholar
• R. Tibshirani, Regression shrinkage and selection via the Lasso, J. R. Stat. Soc. Ser. B 58 (1996), pp. 267–288.
   Google Scholar
• M.J. van de Vijver, Y.D. He, H. Dai, A.A.M. Hart, D.W. Voskuil, G.J. Schreiber, J.L. Peterse, C. Roberts, M.J. Marton, M. Parrish, D. Atsma, A. Witteveen, A. Glas, L. Delahaye, T. van der Velde, H. Bartelink, S. Rodenhuis, E.T. Rutgers, S.H. Friend, and R. Bernards, A gene-expression signature as a predictor of survival in breast cancer, N. Engl. J. Med. 347 (2002), pp. 1999–2009.
   PubMed Web of Science ®Google Scholar
• H. Wang and Y. Xia, Sliced regression for dimension reduction, J. Am. Stat. Assoc. 103 (2008), pp. 811–821.
   Web of Science ®Google Scholar
• Y. Xia, A constructive approach to the estimation of dimension reduction directions, Ann. Statist. 35 (2007), pp. 2654–2690.
   Web of Science ®Google Scholar
• Y. Xia, D. Zhang, and J. Xu, Dimension reduction and semiparametric estimation of survival models, J. Am. Stat. Assoc. 105 (2010), pp. 278–290.
   Web of Science ®Google Scholar
• X. Yan, N. Tang, and X. Zhao, The Spearman rank correlation screening for ultrahigh dimensional censored data, (2017). Available at arXiv:1702.02708v1.
   Google Scholar
• X. Yin and B. Li, Sufficient dimension reduction based on an ensemble of minimum average variance estimators, Ann. Statist. 39 (2011), pp. 3392–3416.
   Web of Science ®Google Scholar
• Z. Yu, Y. Dong, and J. Shao, On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection, Ann. Statist. 44 (2016), pp. 2594–2623.
   Web of Science ®Google Scholar
• J. Zhang, L. Zhu, and L. Zhu, Surrogate dimension reduction in measurement error regressions, Stat. Sin. 24 (2014), pp. 1341–1363.
   Web of Science ®Google Scholar
• L. Zhu, L. Zhu, and Z. Feng, Dimension reduction in regressions through cumulative slicing estimation, J. Am. Stat. Assoc. 105 (2010), pp. 1455–1466.
   Web of Science ®Google Scholar
• Y. Zhu and P. Zeng, Fourier methods for estimating the central subspace and the central mean subspace in regression, J. Am. Stat. Assoc. 101 (2006), pp. 1638–1651.
   Web of Science ®Google Scholar