DocumentCode
1343110
Title
Density estimation from an individual numerical sequence
Author
Nobel, Andrew B. ; Morvai, Gusztav ; Kulkarni, Sanjeev R.
Author_Institution
Dept. of Stat., North Carolina Univ., Chapel Hill, NC, USA
Volume
44
Issue
2
fYear
1998
fDate
3/1/1998 12:00:00 AM
Firstpage
537
Lastpage
541
Abstract
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)
Keywords
estimation theory; parameter estimation; probability; sequences; signal sampling; statistical analysis; L1 consistent estimation; ergodic sample; individual numerical sequence; limiting relative frequencies; probability; statistics; univariate density estimation; upper bound; Convergence; Frequency; Histograms; Kernel; Nearest neighbor searches; Spline; Statistical distributions; Statistics; Stochastic processes; Upper bound;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.661503
Filename
661503
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