Title :
The L1 and L2 strong consistency of recursive kernel density estimation from dependent samples
Author :
Gyorfi, Laszlo ; Masry, Elias
Author_Institution :
Hungarian Acad. of Sci., Tech. Univ. of Budapest, Hungary
fDate :
5/1/1990 12:00:00 AM
Abstract :
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
Keywords :
convergence; information theory; Hilbert space-valued mixingales; L1 strong consistency; L2 strong consistency; convergence rates; dependent samples; ergodic stationary processes; mixing processes; recursive kernel density estimation; Convergence; Hilbert space; Kernel; Markov processes; Particle measurements; Pattern recognition; Probability density function; Recursive estimation; Space stations; Stability;
Journal_Title :
Information Theory, IEEE Transactions on
