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The Bahadur-Kiefer Representation of Lp Regression Estimators

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  • Arcones, Miguel A.

Abstract

We consider the following linear regression model:where are independent and identically distributed random variables, Yi, is real, Zi has values in Rm, Ui, is independent of Zi, and θ0 is an m-dimensional parameter to be estimated. The Lp estimator of θ0 is the value 6n such thatHere, we will give the exact Bahadur-Kiefer representation of θn, for each p ≥ 1. Explicitly, we will see that, under regularity conditions,where and c is a positive constant, which depends on p and on the random variable X.

Suggested Citation

  • Arcones, Miguel A., 1996. "The Bahadur-Kiefer Representation of Lp Regression Estimators," Econometric Theory, Cambridge University Press, vol. 12(2), pages 257-283, June.
    • Handle: RePEc:cup:etheor:v:12:y:1996:i:02:p:257-283_00
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    Cited by:

    1. Du, Jiang & Sun, Zhimeng & Xie, Tianfa, 2013. "M-estimation for the partially linear regression model under monotonic constraints," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1353-1363.
    2. Xuejun Ma & Shaochen Wang & Wang Zhou, 2022. "Statistical inference in massive datasets by empirical likelihood," Computational Statistics, Springer, vol. 37(3), pages 1143-1164, July.
    3. Qifa Xu & Chao Cai & Cuixia Jiang & Fang Sun & Xue Huang, 2020. "Block average quantile regression for massive dataset," Statistical Papers, Springer, vol. 61(1), pages 141-165, February.
    4. He, Xuming & Pan, Xiaoou & Tan, Kean Ming & Zhou, Wen-Xin, 2023. "Smoothed quantile regression with large-scale inference," Journal of Econometrics, Elsevier, vol. 232(2), pages 367-388.
    5. Du, Jiang & Zhang, Zhongzhan & Xie, Tianfa, 2018. "A weighted M-estimator for linear regression models with randomly truncated data," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 90-94.

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