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Transformation-based estimation

Author

Listed:
  • Feng, Zhenghui
  • Wang, Tao
  • Zhu, Lixing
Abstract
To alleviate the computational burden of making the relevant estimation algorithms stable for nonlinear and semiparametric regression models with, particularly, high-dimensional data, a transformation-based method combining sufficient dimension reduction approach is proposed. To this end, model-independent transformations are introduced to models under study. This generic methodology can be applied to transformation models; generalized linear models; and their corresponding quantile regression variants. The constructed estimates almost have closed forms in certain sense such that the above goals can be achieved. Simulation results show that, in finite sample cases with high-dimensional predictors and long-tailed distributions of error, the new estimates often exhibit a smaller degree of variance, and have much less computational burden than the classical methods such as the classical least squares and quantile regression estimation.

Suggested Citation

  • Feng, Zhenghui & Wang, Tao & Zhu, Lixing, 2014. "Transformation-based estimation," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 186-205.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:186-205
    DOI: 10.1016/j.csda.2014.05.001
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    References listed on IDEAS

    as
    1. Yanyuan Ma & Liping Zhu, 2012. "A Semiparametric Approach to Dimension Reduction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 168-179, March.
    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. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    4. Liping Zhu & Tao Wang & Lixing Zhu & Louis Ferré, 2010. "Sufficient dimension reduction through discretization-expectation estimation," Biometrika, Biometrika Trust, vol. 97(2), pages 295-304.
    5. Yanyuan Ma & Liping Zhu, 2013. "Efficiency loss and the linearity condition in dimension reduction," Biometrika, Biometrika Trust, vol. 100(2), pages 371-383.
    6. Yuexiao Dong & Bing Li, 2010. "Dimension reduction for non-elliptically distributed predictors: second-order methods," Biometrika, Biometrika Trust, vol. 97(2), pages 279-294.
    7. Feng, Zhenghui & Zhu, Lixing, 2012. "An alternating determination–optimization approach for an additive multi-index model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1981-1993.
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    Citations

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    Cited by:

    1. Zhu, Xuehu & Wang, Tao & Zhao, Junlong & Zhu, Lixing, 2017. "Inference for biased transformation models," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 105-120.
    2. Kangning Wang & Lu Lin, 2017. "Robust and efficient direction identification for groupwise additive multiple-index models and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 22-45, March.
    3. Chen, Fei & Shi, Lei & Zhu, Xuehu & Zhu, Lixing, 2018. "Generalized principal Hessian directions for mixture multivariate skew elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 142-159.
    4. Jun Zhang & Junpeng Zhu & Zhenghui Feng, 2019. "Estimation and hypothesis test for single-index multiplicative models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 242-268, March.
    5. Tan, Xin Lu, 2019. "Optimal estimation of slope vector in high-dimensional linear transformation models," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 179-204.
    6. Xie, Chuanlong & Zhu, Lixing, 2020. "Generalized kernel-based inverse regression methods for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

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