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Research Article

A model-free conditional screening approach via sufficient dimension reduction

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Pages 970-988 | Received 22 Aug 2019, Accepted 27 Sep 2020, Published online: 03 Nov 2020

References

  • Armesilla, A.L., Calvo, D., and Vega, M.A. (1996), ‘Structural and Functional Characterization of the Human CD36 Gene Promoter’, Journal of Biological Chemistry, 271, 7781–7787. doi: 10.1074/jbc.271.13.7781
  • Barut, E., Fan, J., and Verhasselt, A (2016), ‘Conditional Sure Independence Screening’, Journal of the American Statistical Association, 111, 1266–1277. doi: 10.1080/01621459.2015.1092974
  • Chang, J., Tang, C., and Wu, Y. (2013), ‘Marginal Empirical Likelihood and Sure Independence Feature Screening’, The Annals of Statistics, 41, 1693–2262. doi: 10.1214/13-AOS1139
  • Chang, J., Tang, C., and Wu, Y. (2016), ‘Local Independence Feature Screening for Nonparametric and Semiparametric Models by Marginal Empirical Likelihood’, The Annals of Statistics, 44, 515–539. doi: 10.1214/15-AOS1374
  • Chiaromonte, F., Cook, R.D., and Li, B. (2002), ‘Sufficient Dimension Reduction in Regressions with Categorical Predictors’, The Annals of Statistics, 30, 475–497. doi: 10.1214/aos/1021379862
  • Chu, Y., and Lin, L. (2020), ‘Conditional SIRS for Nonparametric and Semiparametric Models by Marginal Empirical Likelihood’, Statistical Papers, 61, 1589–1606. doi: 10.1007/s00362-018-0993-1
  • Cook, R.D. (1998), Regression Graphics, New York, NY: Wiley.
  • Cook, R.D. (2004), ‘Testing Predictor Contributions in Sufficient Dimension Reduction’, The Annals of Statistics, 32, 1062–1092. doi: 10.1214/009053604000000292
  • Cook, R.D., and Forzani, B. (2009), ‘Likelihood-Based Sufficient Dimension Reduction’, Journal of the American Statistical Association, 104, 197–208. doi: 10.1198/jasa.2009.0106
  • Cook, R.D., and Nachtsheim, C. (1994), ‘Reweighting to Achieve Elliptically Contoured Covariates in Regression’, Journal of the American Statistical Association, 89, 592–599. doi: 10.1080/01621459.1994.10476784
  • Cook, R.D., and Weisberg, S. (1991), ‘Discussion of “sliced Inverse Regression for Dimension Reduction”’, Journal of the American Statistical Association, 86, 328–332.
  • Cui, H., Li, R., and Zhong, W. (2014), ‘Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis’, Journal of the American Statistical Association, 110, 630–641. doi: 10.1080/01621459.2014.920256
  • Dong, Y., and Li, B. (2010), ‘Dimension Reduction for Non-Elliptically Distributed Predictors: Second-Order Methods’, Biometrika, 97, 279–294. doi: 10.1093/biomet/asq016
  • Fan, J., and Lv, J. (2008), ‘Sure Independence Screening for Ultrahigh Dimensional Feature Space (with Discussion)’, Journal of the Royal Statistical: Society Series B, 70, 849–911. doi: 10.1111/j.1467-9868.2008.00674.x
  • Fan, J., and Song, R. (2010), ‘Sure Independence Screening in Generalized Linear Models with NP-dimensionality’, The Annals of Statistics, 38, 3567–3604. doi: 10.1214/10-AOS798
  • Fan, J., Feng, Y., and Song, R. (2011), ‘Nonparametric Independence Screening in Sparse Ultrahigh-Dimensional Additive Models’, Journal of the American Statistical Association, 106, 544–557. doi: 10.1198/jasa.2011.tm09779
  • Feng, Z., Wen, X., Yu, Z., and Zhu, L.-X. (2013), ‘On Partial Sufficient Dimension Reduction With Applications to Partially Linear Multi-Index Models’, Journal of the American Statistical Association, 108, 237–246. doi: 10.1080/01621459.2012.746065
  • Golub, T., Slonim, D., Tamyo, P., Huard, C., Gaasenbeek, M., Mesirov, J., Coller, H., Loh, M., Downing, J., and Caligiuri, M. (1999), ‘Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring’, Science (New York, N.Y.), 286, 531–536. doi: 10.1126/science.286.5439.531
  • Hall, P., and Li, K.C. (1993), ‘On Almost Linearity of Low Dimensional Projection From High Dimensional Data’, The Annals of Statistics, 21, 867–889. doi: 10.1214/aos/1176349155
  • He, X., Wang, L., and Hong, H. (2013), ‘Quantile-Adaptive Model-Free Variable Screening for High-Dimensional Heterogeneous Data’, The Annals of Statistics, 41, 342–369. doi: 10.1214/13-AOS1087
  • Hilafu, H., and Wu, W (2017), ‘Partial Projective Resampling Method for Dimension Reduction: With Applications to Partially Linear Models’, Computational Statistics and Data Analysis, 109, 1–14. doi: 10.1016/j.csda.2016.12.002
  • Hong, H.G., Wang, L., and He, X. (2016), ‘A Data-Driven Approach to Conditional Screening of High-Dimensional Variables’, Stat, 5, 200–212. doi: 10.1002/sta4.115
  • Jiang, B., and Liu, J.S. (2013), ‘Sliced Inverse Regression With Variable Selection and Interaction Detection’, Manuscript.
  • Li, K.C. (1991), ‘Sliced Inverse Regression for Dimension Reduction (with Discussion)’, Journal of the American Statistical Association, 86, 316–327. doi: 10.1080/01621459.1991.10475035
  • Li, B., and Dong, Y. (2009), ‘Dimension Reduction for Non-Elliptically Distributed Predictors’, The Annals of Statistics, 37, 1272–1298. doi: 10.1214/08-AOS598
  • Li, B., and Wang, S. (2007), ‘On Directional Regression for Dimension Reduction’, Journal of the American Statistical Association, 102, 997–1008. doi: 10.1198/016214507000000536
  • Li, B., Kim, M.K., and Altman, N. (2010), ‘On Dimension Folding of Matrix Or Array Valued Statistical Objects’, The Annals of Statistics, 38, 1097–1121.
  • Lin, L., Sun, J., and Zhu, L.-X. (2013), ‘Nonparametric Feature Screening’, Computational Statistics and Data Analysis, 67, 162–174. doi: 10.1016/j.csda.2013.05.016
  • Lu, J., and Lin, L. (2020), ‘Model-Free Conditional Screening Via Conditional Distance Correlation’, Statistical Papers, 61, 225–244. doi: 10.1007/s00362-017-0931-7
  • Mai, Q., and Zou, H. (2013), ‘The Kolmogorov Filter for Variable Screening in High-Dimensional Binary Classification’, Biometrika, 100, 229–234. doi: 10.1093/biomet/ass062
  • Mai, Q., and Zou, H. (2015), ‘The Fused Kolmogorov Filter: A Nonparametric Model-Free Screening Method’, The Annals of Statistics, 43, 1471–1497. doi: 10.1214/14-AOS1303
  • Niu, Y., Zhang, R., Liu, J., and Li, H. (2020), ‘Group Screening for Ultra-High-Dimensional Feature Under Linear Model’, Statistical Theory and Related Fields, 4, 43–54. doi: 10.1080/24754269.2019.1633763
  • Pan, R., Wang, H., and Li, R. (2015), ‘Ultrahigh Dimensional Multi-Class Linear Discriminant Analysis by Pairwise Sure Independence Screening’, Journal of the American Statistical Association., 111, 169–179. doi: 10.1080/01621459.2014.998760
  • Shao, Y., Cook, R.D., and Weisberg, S. (2007), ‘Marginal Tests with Sliced Average Variance Estimation’, Biometrika, 94, 285–296. doi: 10.1093/biomet/asm021
  • Wang, H. (2009), ‘Forward Regression for Ultra-High Dimensional Variable Screening’, Journal of the American Statistical Association, 104, 1512–1524. doi: 10.1198/jasa.2008.tm08516
  • Wang, H. (2012), ‘Factor Profiled Sure Independence Screening’, Biometrika, 99, 15–28. doi: 10.1093/biomet/asr074
  • Xue, L., and Zou, H. (2011), ‘Sure Independence Screening and Compressed Random Sensing’, Biometrika, 98, 371–380. doi: 10.1093/biomet/asr010
  • Yu, Z., Dong, Y., and Zhu, L.-X. (2016), ‘Trace Pursuit: a General Framework for Model-Free Variable Selection’, Journal of the American Statistical Association, 111, 813–821. doi: 10.1080/01621459.2015.1050494
  • Zhao, S.D., and Li, Y. (2012), ‘Sure Screening for Estimating Equations in Ultra-High Dimensions’, Manuscript.
  • Zhong, W., Zhang, T., Zhu, M., and Liu, J.S. (2012), ‘Correlation Pursuit: Forward Stepwise Variable Selection for Index Models’, Journal of Royal Statistical Society: Series B, 74, 849–870. doi: 10.1111/j.1467-9868.2011.01026.x
  • Zhu, L., Li, L., Li, R., and Zhu, L.-X. (2011), ‘Model-Free Feature Screening for Ultrahigh Dimensional Data’, Journal of American Statistical Association, 106, 1464–1475. doi: 10.1198/jasa.2011.tm10563

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