DocumentCode
941004
Title
On nonparametric estimation of a functional of a probability density
Author
Pawlak, Miroslaw
Volume
32
Issue
1
fYear
1986
fDate
1/1/1986 12:00:00 AM
Firstpage
79
Lastpage
84
Abstract
The nonparametric estimate derived from the Hermite orthogonal system of the functional 
where 
is an unknown probability density, is studied. Sufficient conditions for the weak and strong consistency of the estimate are presented, and the rate of convergence is given. In particular, under mild assumptions on , the rate of mean-square error convergence is 
, whereas for almost complete convergence it is 
. Moreover, several possible applications in the area of nonparametric inference of the estimate are indicated.
where is an unknown probability density, is studied. Sufficient conditions for the weak and strong consistency of the estimate are presented, and the rate of convergence is given. In particular, under mild assumptions on , the rate of mean-square error convergence is , whereas for almost complete convergence it is . Moreover, several possible applications in the area of nonparametric inference of the estimate are indicated.Keywords
Estimation; Probability; Convergence; Distribution functions; Kernel; Random variables; Signal detection; Statistical analysis; Statistical distributions; Statistics; Sufficient conditions; Testing;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.1986.1057120
Filename
1057120
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