Density estimation from an individual numerical sequence

Details Density estimation from an individual numerical sequence Density estimation from an individual numerical sequence

2007-10-12

arxiv.org/abs/0710.2500v1

IEEE Trans. Inform. Theory 44 (1998), no. 2, 537--541

Mathematics

Probability

Scientific paper

This paper considers estimation of a univariate density from an individual numerical sequence. It is assumed that (i) the limiting relative frequencies of the numerical sequence are governed by an unknown density, and (ii) 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 $L_1$ consistent when (i) and (ii) apply. In addition it is shown that there is no consistent estimation scheme for the set of individual sequences satisfying only condition (i).

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