Density estimation from an individual numerical sequence
Probability
2008-06-19 v1 Information Theory
math.IT
Statistics Theory
Statistics Theory
Abstract
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 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).
Cite
@article{arxiv.0710.2500,
title = {Density estimation from an individual numerical sequence},
author = {Andrew B. Nobel and Gusztav Morvai and Sanjeev R. Kulkarni},
journal= {arXiv preprint arXiv:0710.2500},
year = {2008}
}