L. I. PITERBARG
Copyright © 2013 SciRes. AM
1277
want to stress two of them, first, for high
e and, second,
Fuzzy 2 is
uniformly better than any other estimat0
ˆ
is not appropriate for such values of
regardless
noise distribution.
4. Conclusions and Discussion
A majority of studies in estimating a location parameter
address, first, linear functionals of either the original
sample or its ranking, e.g. [11], and, second, unbiased
observations. Here a class of essentially nonlinear esti-
mators is suggested based on the fuzzy set theory ideas to
handle biased observations coming from two different
sources. Because any analytical investigation of the
standard error for highly non-linear functions of sample
an the classical least square estimator.
r
are estimator and
N00014-11-1-0369 and NSF under grant CMG-1025453
is greatly appreciated.
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M-
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its modifications for essential bias and high level of noise.
Moreover, even for small bias, the fuzzy estimators are
only slightly worse than the optimal one.
Unexpectedly, the primitive arithmetic mean succes-
fully competes with fuzzy estimators for essential biases
and modest noise level, but it is of little help for high
level of noise or negligable biases.
Notice that the developed fuzzy estimators are highly
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tro
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[10] K. Deb, “Multi-Objective Optimization Using Evolution-
ary Alg
duced here. It would be interesting to find an optimal
one among them. Another important problem is to ad-
dress a similar problem for more than two information
sources.
5. Acknowledgements
The support of the Office of Naval Research under grant
orithms,” Willey, Princeton, 2001.
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ter,” The Annals of Mathematical Statistics, Vol. 35, No.
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