DocumentCode :
917874
Title :
Estimation of the mean with time-varying finite memory (Corresp.)
Author :
Wagner, Terry J.
Volume :
18
Issue :
4
fYear :
1972
fDate :
7/1/1972 12:00:00 AM
Firstpage :
523
Lastpage :
525
Abstract :
Let 
be a sequence of independent identically distributed observations with a common mean 
. Assume that 
with probability 1. We show that for each 
there exists an integer 
, a finite-valued statistic 
and a real-valued function 
defined on 
such that 
) 
; ii) ![P[\\lim \\sup \\mid d(T_n) - \\mu \\mid \\leq \\varepsilon ] = 1](/images/tex/7733.gif)
. Thus we have a recursive-like estimate of , for which the data are summarized for each 
by one of states and which converges to within 
of with probability 1. The constraint on memory here is time varying as contrasted to the time-invariant constraint that would have 
for all .
be a sequence of independent identically distributed observations with a common mean . Assume that with probability 1. We show that for each there exists an integer , a finite-valued statistic and a real-valued function defined on such that ) ; ii) . Thus we have a recursive-like estimate of , for which the data are summarized for each by one of states and which converges to within of with probability 1. The constraint on memory here is time varying as contrasted to the time-invariant constraint that would have for all .Keywords :
Estimation; Finite-memory methods; Band pass filters; Bandwidth; Binary codes; Electrons; Gaussian processes; Pulse modulation; Quantization; Sampling methods; Solids; Telecommunications;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1972.1054853
Filename :
1054853
Link To Document :
