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Estimation for single-index models via martingale difference divergence

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  • Liu, Jicai
  • Xu, Peirong
  • Lian, Heng

Abstract

In this paper, we focus on the estimation of the index coefficients in single-index models and develop a new procedure based on martingale difference divergence. Since the proposed procedure can capture automatically the conditional mean dependence of the response variable on the covariates, it does not involve smoothing techniques or require the commonly used assumptions in the literature of single-index models, such as smooth link functions and at least one continuous covariate. Under some mild conditions, we establish the asymptotic normality of the estimators. We assess the finite sample performance of the proposed procedure by Monte Carlo simulation studies. We further illustrate the proposed method through empirical analyses of a real dataset.

Suggested Citation

  • Liu, Jicai & Xu, Peirong & Lian, Heng, 2019. "Estimation for single-index models via martingale difference divergence," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 271-284.
    • Handle: RePEc:eee:csdana:v:137:y:2019:i:c:p:271-284
    DOI: 10.1016/j.csda.2019.03.008
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    References listed on IDEAS

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    1. Chung Eun Lee & Xiaofeng Shao, 2018. "Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Stationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 216-229, January.
    2. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    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. Sheng, Wenhui & Yin, Xiangrong, 2013. "Direction estimation in single-index models via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 148-161.
    5. Yanyuan Ma & Liping Zhu, 2013. "Doubly robust and efficient estimators for heteroscedastic partially linear single-index models allowing high dimensional covariates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 305-322, March.
    6. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    7. Xiaofeng Shao & Jingsi Zhang, 2014. "Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1302-1318, September.
    8. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
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    Cited by:

    1. Lai, Tingyu & Zhang, Zhongzhan & Wang, Yafei, 2021. "A kernel-based measure for conditional mean dependence," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).

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