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Sequential nonparametric density estimation

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2 Author(s)

Using kernel estimates of the Parzen type, a naive sequential nonparametric density estimation procedure is developed. The asymptotic distribution structure of the stopping variable is examined. The stopping variable is shown to have finite moments of ail order and is shown to be dosed. The stopping variableNdepends on some preassigned errorvarepsilon, and it is shown thatNdiverges strongly toinftyasvarepsilonconverges to zero. Finally, withhat{f}_n(x)being a kernel-type estimator, it is shown thathat{f}_N(X)converges tof(x), the true density atx, with probability one asvarepsilonconverges to zero.

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Information Theory, IEEE Transactions on  (Volume:21 ,  Issue: 6 )