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Feature Screening for Ultrahigh Dimensional Categorical Data With Applications

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  • Danyang Huang
  • Runze Li
  • Hansheng Wang

Abstract

Ultrahigh dimensional data with both categorical responses and categorical covariates are frequently encountered in the analysis of big data, for which feature screening has become an indispensable statistical tool. We propose a Pearson chi-square based feature screening procedure for categorical response with ultrahigh dimensional categorical covariates. The proposed procedure can be directly applied for detection of important interaction effects. We further show that the proposed procedure possesses screening consistency property in the terminology of Fan and Lv (2008). We investigate the finite sample performance of the proposed procedure by Monte Carlo simulation studies and illustrate the proposed method by two empirical datasets.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:2:p:237-244
    DOI: 10.1080/07350015.2013.863158
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    References listed on IDEAS

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    1. Wang, Hansheng, 2007. "A note on iterative marginal optimization: a simple algorithm for maximum rank correlation estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2803-2812, March.
    2. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
    3. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    4. 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.
    5. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    6. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    7. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    8. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-137, January.
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    Citations

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    Cited by:

    1. Lu, Jun & Lin, Lu & Wang, WenWu, 2021. "Partition-based feature screening for categorical data via RKHS embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Ji Chen & Jun Shao & Fang Fang, 2021. "Instrument search in pseudo-likelihood approach for nonignorable nonresponse," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 519-533, June.
    3. Xiong, Wei & Chen, Yaxian & Ma, Shuangge, 2023. "Unified model-free interaction screening via CV-entropy filter," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    4. Baiguo An & Guozhong Feng & Jianhua Guo, 2022. "Interaction Identification and Clique Screening for Classification with Ultra-high Dimensional Discrete Features," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 122-146, March.
    5. Shuaishuai Chen & Jun Lu, 2023. "Quantile-Composited Feature Screening for Ultrahigh-Dimensional Data," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    6. 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.
    7. Sweata Sen & Damitri Kundu & Kiranmoy Das, 2023. "Variable selection for categorical response: a comparative study," Computational Statistics, Springer, vol. 38(2), pages 809-826, June.
    8. 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.
    9. Sheng, Ying & Wang, Qihua, 2020. "Conditional probability estimation based classification with class label missing at random," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    10. Zhao, Shaofei & Fu, Guifang, 2022. "Distribution-free and model-free multivariate feature screening via multivariate rank distance correlation," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    11. Randall Reese & Guifang Fu & Geran Zhao & Xiaotian Dai & Xiaotian Li & Kenneth Chiu, 2022. "Epistasis Detection via the Joint Cumulant," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 514-532, December.
    12. Yuan, Qingcong & Chen, Xianyan & Ke, Chenlu & Yin, Xiangrong, 2022. "Independence index sufficient variable screening for categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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