ASYMPTOTICS FOR THE DISTRIBUTION FUNCTION ESTIMATORS OF THE ERRORS IN SEMI-PARAMETRIC REGRESSION MODELS

QIU Yuyang , FU Keang , HUANG Wei

Journal of Systems Science & Complexity ›› 2014, Vol. 27 ›› Issue (2) : 360-369.

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Journal of Systems Science & Complexity ›› 2014, Vol. 27 ›› Issue (2) : 360-369. DOI: 10.1007/s11424-014-2255-1
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ASYMPTOTICS FOR THE DISTRIBUTION FUNCTION ESTIMATORS OF THE ERRORS IN SEMI-PARAMETRIC REGRESSION MODELS

  • QIU Yuyang1 , FU Keang 1, HUANG Wei2
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Abstract

This paper considers the convergence rates for nonparametric estimators of the error distribution in semi-parametric regression models. By establishing some general laws of the iterated logarithm, it shows that the rates of convergence of either the empirical distribution or a smoothed version of the empirical distribution function matches exactly the rates obtained for an independent sample from the error distribution.

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QIU Yuyang , FU Keang , HUANG Wei. ASYMPTOTICS FOR THE DISTRIBUTION FUNCTION ESTIMATORS OF THE ERRORS IN SEMI-PARAMETRIC REGRESSION MODELS. Journal of Systems Science and Complexity, 2014, 27(2): 360-369 https://doi.org/10.1007/s11424-014-2255-1

Funding

This research was supported by the National Science Foundation of China under Grant Nos. 11201422,11301481, and 11371321, Zhejiang Provincial Natural Science Foundation of China under Grant Nos. Y6110639, Y6110110, LQ12A01018, and LQ12A01017, the National Statistical Science Research Project of China under Grant No. 2012LY174, Foundation for Young Talents of ZJGSU under Grant No. 1020XJ1314019, and Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics).

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