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Error density estimation in high-dimensional sparse linear model

Author

Listed:
  • Feng Zou

    (Capital Normal University)

  • Hengjian Cui

    (Capital Normal University)

Abstract

This paper is concerned with the error density estimation in high-dimensional sparse linear model, where the number of variables may be larger than the sample size. An improved two-stage refitted cross-validation procedure by random splitting technique is used to obtain the residuals of the model, and then traditional kernel density method is applied to estimate the error density. Under suitable sparse conditions, the large sample properties of the estimator including the consistency and asymptotic normality, as well as the law of the iterated logarithm are obtained. Especially, we gave the relationship between the sparsity and the convergence rate of the kernel density estimator. The simulation results show that our error density estimator has a good performance. A real data example is presented to illustrate our methods.

Suggested Citation

  • Feng Zou & Hengjian Cui, 2020. "Error density estimation in high-dimensional sparse linear model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(2), pages 427-449, April.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:2:d:10.1007_s10463-018-0699-0
    DOI: 10.1007/s10463-018-0699-0
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    References listed on IDEAS

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    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    5. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Jianqing Fan & Shaojun Guo & Ning Hao, 2012. "Variance estimation using refitted cross‐validation in ultrahigh dimensional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(1), pages 37-65, January.
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