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.

REFERENCES

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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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We tested only two estimators from a wide class in-

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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