DENSITY-ESTIMATION FROM AN INDIVIDUAL NUMERICAL SEQUENCE

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