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Statistical estimation in partially linear single-index models with error-prone linear covariates

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  • Zhensheng Huang

Abstract

This article considers a class of partially linear single-index models when some linear covariates are not observed, but their ancillary variables are available. This model can avoid the ‘curse of dimensionality’ in multivariate nonparametric regressions, and it contains many existing statistical models such as the partially linear model (Engle, R.F., Granger, W. J., Rice, J., and Weiss, A. (1986), ‘Semiparametric Estimates of the Relation Between Weather and Electricity Sales’, Journal of The American Statistical Association, 80, 310–319), the single-index model (Härdle, W., Hall, P., and Ichimura, H. (1993), ‘Optimal Smoothing in Single-Index Models’, The Annals of Statistics, 21, 157–178), the partially linear errors-in-variables model (Liang, H., Härdle, W., and Carroll, R.J. (1999), ‘Estimation in a Semi-parametric Partially Linear Errors-in-Variables Model’, The Annals of Statistics, 27, 1519–1535), the partially linear single-index measurement error model (Liang, H., and Wang, N. (2005), ‘Partially Linear Single-Index Measurement Error Models’, Statistica Sinica, 15, 99–116), and so on as special examples. In this article, an estimation procedure for the unknowns of the proposed models is proposed, and asymptotic properties of the corresponding estimators are derived. Finite sample performance of the proposed methodology is assessed by Monte Carlo simulation studies. A real example is also given to illustrate the proposed procedures.

Suggested Citation

  • Zhensheng Huang, 2011. "Statistical estimation in partially linear single-index models with error-prone linear covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 339-350.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:2:p:339-350
    DOI: 10.1080/10485252.2010.518705
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    References listed on IDEAS

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    1. Lu, Xuewen & Cheng, Tsung-Lin, 2007. "Randomly censored partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1895-1922, November.
    2. Lixing Zhu & Liugen Xue, 2006. "Empirical likelihood confidence regions in a partially linear single‐index model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 549-570, June.
    3. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    4. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
    5. 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. Huang, Zhensheng & Pang, Zhen & Hu, Tao, 2013. "Testing structural change in partially linear single-index models with error-prone linear covariates," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 121-133.

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