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Adjusted Pearson Chi-Square feature screening for multi-classification with ultrahigh dimensional data

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  • Lyu Ni

    (East China Normal University)

  • Fang Fang

    (East China Normal University)

  • Fangjiao Wan

    (East China Normal University)

Abstract

Huang et al. (J Bus Econ Stat 32:237–244, 2014) first proposed a Pearson Chi-Square based feature screening procedure tailored to multi-classification problem with ultrahigh dimensional categorical covariates, which is a common problem in practice but has seldom been discussed in the literature. However, their work establishes the sure screening property only in a limited setting. Moreover, the p value based adjustments when the number of categories involved by each covariate is different do not work well in several practical situations. In this paper, we propose an adjusted Pearson Chi-Square feature screening procedure and a modified method for tuning parameter selection. Theoretically, we establish the sure screening property of the proposed method in general settings. Empirically, the proposed method is more successful than Pearson Chi-Square feature screening in handling non-equal numbers of covariate categories in finite samples. Results of three simulation studies and one real data analysis are presented. Our work together with Huang et al. (J Bus Econ Stat 32:237–244, 2014) establishes a solid theoretical foundation and empirical evidence for the family of Pearson Chi-Square based feature screening methods.

Suggested Citation

  • Lyu Ni & Fang Fang & Fangjiao Wan, 2017. "Adjusted Pearson Chi-Square feature screening for multi-classification with ultrahigh dimensional data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 805-828, November.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0629-9
    DOI: 10.1007/s00184-017-0629-9
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    References listed on IDEAS

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    1. Rui Pan & Hansheng Wang & Runze Li, 2016. "Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 169-179, March.
    2. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    3. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    4. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    5. Lyu Ni & Fang Fang, 2016. "Entropy-based model-free feature screening for ultrahigh-dimensional multiclass classification," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 515-530, September.
    6. Danyang Huang & Runze Li & Hansheng Wang, 2014. "Feature Screening for Ultrahigh Dimensional Categorical Data With Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 237-244, April.
    7. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    8. Qing Mai & Hui Zou, 2013. "The Kolmogorov filter for variable screening in high-dimensional binary classification," Biometrika, Biometrika Trust, vol. 100(1), pages 229-234.
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    Cited by:

    1. Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.

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