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Nonparametric feature screening. (English) Zbl 06970880
Summary: The measure of correlation between response and predictors plays a critical role in feature ranking and screening for nonparametric regression models. In this paper, a nonparametric function-correlative feature screening is introduced. The newly proposed method does not need any assumption on structural relationships between response and predictors, and among predictors. By using local information flows of model variables, the function-correlation between response and predictors is captured successfully. Selection consistency is achieved as well. Simulation studies are carried out to examine the performance of the new method.

##### MSC:
 62 Statistics
Full Text:
##### References:
 [1] Fan, J.; Feng, Y.; Song, R., Nonparametric independence screening in sparse ultra-high-dimensional additive models, J. Amer. Statist. Assoc. Ser. B, 106, 544-557, (2011) · Zbl 1232.62064 [2] Fan, J.; Feng, Y.; Wu, Y., High-dimensional variable selection for cox’s proportional hazards model, (IMS Collections, Borrowing Strength: Theory Powering Applications—A Festschrift for Lawrence D. Brown, Vol. 6, (2010)), 70-86 [3] Fan, J.; Lv, J., Sure independence screening for ultrahigh dimensional feature space (with discussion), J. R. Stat. Soc. Ser. B, 70, 849-911, (2008) [4] Fan, J.; Samworth, R.; Wu, Y., Ultrahigh dimensional feature selection: beyond the linear model, J. Mach. Learn. Res., 10, 1829-1853, (2009) [5] Fan, J.; Song, R., Sure independence screening in generalized linear models with NP-dimensionality, Ann. Statist., 38, 3567-3604, (2010) · Zbl 1206.68157 [6] Li, G. R.; Peng, H.; Zhang, J.; Zhu, L. X., Robust rank correlation based screening, Ann. Statist., 40, 1846-1877, (2012) · Zbl 1257.62067 [7] Li, R.; Zhong, W.; Zhu, L. P., Feature screening via distance correlation learning, J. Amer. Statist. Assoc., (2012), (in press) · Zbl 1443.62184 [8] Luo, X.; Stefanski, L. A.; Boos, D. D., Tuning variable selection procedure by adding noise, Technometrics, 48, 165-175, (2006) [9] Zhu, L. P.; Li, L. X.; Li, R.; Zhu, L. X., Model-free feature screening for ultrahigh-dimensional data, J. Amer. Statist. Assoc., 106, 1464-1474, (2011) · Zbl 1233.62195 [10] Zhu, L. P.; Zhu, L. X., On distribution-weighted partial least squares with diverging number of highly correlated predictors, J. R. Stat. Soc. Ser. B, 71, 525-548, (2009) · Zbl 1248.62097 [11] Zhu, L. P.; Zhu, L. X.; Ferré, L.; Wang, T., Sufficient dimension reduction through discretization-expectation estimation, Biometrika, 97, 295-304, (2010) · Zbl 1205.62048
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