Abstract
Dimension reduction is a crucial issue for high-dimensional data analysis. When the correlation among the variables is strong, the original SIRS (Zhu et al. in J Am Stat Assoc 106(496):1464–1475, 2011) may lose efficiency. Under high-dimensional setting, eliminating the bad influence caused by the correlation has become an important issue. Aiming at this issue, we propose a feature screening approach by combining the marginal empirical likelihood with the conditional SIRS. Based on a centralized SIRS, the correlation among the variables is significantly reduced and consequently, the related empirical likelihood is improved remarkably. Moreover, our method is model-free due to the properties of SIRS and empirical likelihood. The proposed method can select important predictors directly without parameter estimation, implying that the method is computationally simple. Under some general conditions, the proposed marginal empirical likelihood ratio is self-studentized. The simulation study shows that compared with other unconditional and conditional methods, our method is competitive and has a great superiority.
Similar content being viewed by others
References
Barut E, Fan J, Verhasselt A (2016) Conditional sure independence screening. J Am Stat Assoc 111(515):1266–1277
Breiman L (1995) Better subset regression using the nonnegative garrote. Technometrics 37(4):373–384
Candes E, Tao T (2007) The dantzig selector: statistical estimation when p is much larger than n. Ann Stat 35(6):2313–2351
Chang J, Tang CY, Wu Y (2013) Marginal empirical likelihood and sure independence feature screening. Ann Stat 41(4):2133–2148
Chang J, Tang CY, Wu Y (2016) Local independence feature screening for nonparametric and semiparametric models by marginal empirical likelihood. Ann Stat 44(2):515–539
Chen J, Variyath AM, Abraham B (2008) Adjusted empirical likelihood and its properties. J Comput Graph Stat 17(2):426–443
Efron B, Hastie T, Johnstone I et al (2004) Least angle regression. Ann Stat 32(2):407–499
Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96(456):1348–1360
Fan J, Lv J (2008) Sure independence screening for ultrahigh dimensional feature space. J R Stat Soc B 70(5):849–911
Fan J, Song R (2010) Sure independence screening in generalized linear models with NP-dimensionality. Ann Stat 38(6):3567–3604
Fan J, Ma Y, Dai W (2014) Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models. J Am Stat Assoc 109(507):1270–1284
Frank LLE, Friedman JH (1993) A statistical view of some chemometrics regression tools. Technometrics 35(2):109–135
Golub T, Slonim D, Tamayo P et al (1999) Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. Science 286(5439):531–537
He X, Wang L, Hong H et al (2013) Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data. Ann Stat 41(1):342–369
Hu Q, Lin L (2017) Conditional sure independence screening by conditional marginal empirical likelihood. Ann Inst Stat Math 69(1):63–96
Li R, Zhong W, Zhu L (2012) Feature screening via distance correlation learning. J Am Stat Assoc 107(499):1129–1139
Lin L, Sun J (2016) Adaptive conditional feature screening. Comput Stat Data Anal 94:287–301
Lin L, Sun J, Zhu L (2013) Nonparametric feature screening. Comput Stat Data Anal 67:162–174
Liu J, Li R, Wu R (2014) Feature selection for varying coefficient models with ultrahigh-dimensional covariates. J Am Stat Assoc 109(505):266–274
Lu J , Lin L (2017) Model-free conditional screening via conditional distance correlation. Stat Pap https://doi.org/10.1007/s00362-017-0931-7
Owen AB (1988) Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75(2):237–249
Owen AB (1990) Empirical likelihood ratio confidence regions. Ann Stat 18:90–120
Owen AB (2001) Empirical likelihood. Chapman & Hall/CRC, New York
Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc B 58(1):267–288
Wang M , Tian G (2017) Adaptive group lasso for high-dimensional generalized linear models. Stat Pap https://doi.org/10.1007/s00362-017-0882-z
Wang H, Li G, Jiang G (2007) Robust regression shrinkage and consistent variable selection through the LAD-Lasso. J Bus Econ Stat 25(3):347–355
Wu S, Xue H, Wu Y et al (2014) Variable selection for sparse high-dimensional nonlinear regression models by combining nonnegative garrote and sure independence screening. Stat Sin 24(3):1365–1387
Xu C, Chen J (2014) The sparse MLE for ultrahigh-dimensional feature screening. J Am Stat Assoc 109(507):1257–1269
Zhu LP, Li L, Li R et al (2011) Model-free feature screening for ultrahigh-dimensional data. J Am Stat Assoc 106(496):1464–1475
Zou H (2006) The adaptive lasso and its oracle properties. J Am Stat Assoc 101(476):1418–1429
Zou H, Yuan M (2008) Composite quantile regression and the oracle model selection theory. Ann Stat 36:1108–1126
Acknowledgements
We thank Wenwu Wang and Jun Lu for their constructive suggestion and efforts to this article. Our deepest gratitude goes to the anonymous reviewers and editors for their careful work and thoughtful suggestions on improving this paper substantially. The research was supported by NNSF Projects (11571204 and 11231005) of China.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Chu, Y., Lin, L. Conditional SIRS for nonparametric and semiparametric models by marginal empirical likelihood. Stat Papers 61, 1589–1606 (2020). https://doi.org/10.1007/s00362-018-0993-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-018-0993-1