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The L1 and L2 strong consistency of recursive kernel density estimation from dependent samples

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2 Author(s)
Gyorfi, L. ; Hungarian Acad. of Sci., Tech. Univ. of Budapest, Hungary ; Masry, E.

The L1 and L2 strong consistency of recursive kernel density estimators is established for mixing and ergodic stationary processes. Sharp rates of almost sure convergence are obtained in the L2 case for mixing processes. In addition, the concept and properties of Hilbert space-valued mixingales are developed, and strong laws of large numbers are given

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Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 3 )