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Moment convergence of regularized least-squares estimator for linear regression model

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  • Yusuke Shimizu

    (Kyushu University)

Abstract

In this paper, we study the uniform tail-probability estimates of a regularized least-squares estimator for the linear regression model. We make use of the polynomial type large deviation inequality for the associated statistical random fields, which may not be locally asymptotically quadratic. Our results enable us to verify various arguments requiring convergence of moments of estimator-dependent statistics, such as the mean squared prediction error and the bias correction for AIC-type information criterion.

Suggested Citation

  • Yusuke Shimizu, 2017. "Moment convergence of regularized least-squares estimator for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1141-1154, October.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:5:d:10.1007_s10463-016-0577-6
    DOI: 10.1007/s10463-016-0577-6
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    References listed on IDEAS

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    1. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(3), pages 431-479, June.
    2. 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.
    3. Yuji Sakamoto & Nakahiro Yoshida, 2004. "Asymptotic expansion formulas for functionals of ε-Markov processes with a mixing property," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 545-597, September.
    4. Masayuki Uchida & Nakahiro Yoshida, 2001. "Information Criteria in Model Selection for Mixing Processes," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 73-98, January.
    5. Findley, David F. & Wei, Ching-Zong, 2002. "AIC, Overfitting Principles, and the Boundedness of Moments of Inverse Matrices for Vector Autotregressions and Related Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 415-450, November.
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