Journal of Theoretical Probability

, Volume 21, Issue 2, pp 267–286 | Cite as

A Note on Asymptotic Normality of Kernel Estimation for Linear Random Fields on Z 2

  • Tsung-Lin Cheng
  • Hwai-Chung Ho
  • Xuewen Lu


This note considers the kernel estimation of a linear random field on Z 2. Instead of imposing certain mixing conditions on the random fields, it is assumed that the weights of the innovations satisfy a summability property. By building a martingale decomposition based on a suitable filtration, asymptotic normality is proven for the kernel estimator of the marginal density of the random field.


Central limit theorem Kernel estimation Linear random field 

Mathematics Subject Classification (2000)

60F05 62G07 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsNational Changhua University of EducationChanghuaTaiwan
  2. 2.Institute of Statistical Science, Academia Sinica and Department of FinanceNational Taiwan UniversityTaipeiTaiwan
  3. 3.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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