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Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case

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  • Bai, Z. D.
  • Wu, Y.

Abstract

Asymptotics of M-estimators of the regression coefficients in linear models (both scale-variant and scale-invariant) when the number of regression coefficients tends to infinity as the sample size increases are investigated The main purpose of this study is to establish the asymptotic properties under weaker conditions than usually assumed, especially to relax the restrictions on the order of the dimension. Also, the conditions assumed and the results obtained seem easy to be extended to the multivariate linear models. In the first part of the paper, the asymptotic behavior of the ordinary (i.e., not scale-invariant) M-estimates is considered.

Suggested Citation

  • Bai, Z. D. & Wu, Y., 1994. "Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 211-239, November.
    • Handle: RePEc:eee:jmvana:v:51:y:1994:i:2:p:211-239
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    Cited by:

    1. Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    2. Miaomiao Wang & Xinyu Zhang & Alan T. K. Wan & Kang You & Guohua Zou, 2023. "Jackknife model averaging for high‐dimensional quantile regression," Biometrics, The International Biometric Society, vol. 79(1), pages 178-189, March.
    3. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    4. Ding, Hao & Qin, Shanshan & Wu, Yuehua & Wu, Yaohua, 2021. "Asymptotic properties on high-dimensional multivariate regression M-estimation," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    5. Ioannis Kalogridis, 2022. "Asymptotics for M-type smoothing splines with non-smooth objective functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 373-389, June.
    6. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    7. He, Xuming & Shao, Qi-Man, 2000. "On Parameters of Increasing Dimensions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 120-135, April.
    8. Ding, Hao & Wang, Zhanfeng & Wu, Yaohua, 2017. "Tobit regression model with parameters of increasing dimensions," Statistics & Probability Letters, Elsevier, vol. 120(C), pages 1-7.
    9. Zhou, Ping & Yu, Zhen & Ma, Jingyi & Tian, Maozai & Fan, Ye, 2021. "Communication-efficient distributed estimator for generalized linear models with a diverging number of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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