Title :
Density estimation from an individual numerical sequence
Author :
Nobel, A.B. ; Morvai, G. ; Kulkarni, S.R.
Author_Institution :
Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA
Abstract :
The article considers univariate density estimation 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 an an increasing sequence of intervals. A simple estimation scheme is proposed, and its L1 consistency is established 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)
Keywords :
parameter estimation; probability; sequences; consistent estimation; density variation; individual numerical sequence; limiting relative frequencies; probability; univariate density estimation; upper bound; Density functional theory; Density measurement; Estimation theory;
Conference_Titel :
Information Theory, 1998. Proceedings. 1998 IEEE International Symposium on
Conference_Location :
Cambridge, MA
Print_ISBN :
0-7803-5000-6
DOI :
10.1109/ISIT.1998.708960
