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Density estimation from an individual numerical sequence

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3 Author(s)
Nobel, A.B. ; Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA ; Morvai, G. ; Kulkarni, S.R.

This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (1) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (2) there is a known upper bound for the variation of the density on an increasing sequence of intervals. A simple estimation scheme is proposed, and is shown to be L1 consistent when (1) and (2) apply. In addition, it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (1)

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 2 )