Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (3): 547-556.

• Articles • Previous Articles     Next Articles

Asymptotic Properties of Conditional Density Estimation for Dependence Functional Data

 LING Neng-Xiang, DING Jie   

  1. School of Mathematics, Hefei University of Technology, Hefei 230009
  • Received:2010-05-10 Revised:2011-11-26 Online:2012-06-25 Published:2012-06-25
  • Supported by:

    国家自然科学基金(11171001)、教育部人文社科规划基金(10YJA910005)、安徽省自然科学基金(11040606M03)、教育部科学技术研究重大项目(309017)和安徽省教育厅重点科研基金项目(KJ2010A282)资助

Abstract:

In this paper, we investigate the almost uniform complete convergence of nonparametric conditional density estimation for functional data by the Kolmogorov's entropy in some semi-metric functional space and obtain the uniform almost complete convergence rate of the estimator  under dependent case, which extend the i.i.d.  functional data to the dependence setting. At the same time,  the asymptotic normal of the estimator is also established  in this case.

Key words: Dependence functional data, Entropy, Rate of uniform almost complete convergence, Conditional , density

CLC Number: 

  • 62G07
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