committees

[Michael P. Perrone]

Scott Farrar writes:
-->John Hampshire characterized a committee as a collection of biased
-->estimators; the idea being that a collection of many different kinds of
-->bias might constitute a unbiased estimator.  I was wondering if anyone
-->had any ideas about how this might be related to, supported by, or refuted
-->by the Central Limit Theorem.  Could experimental variances or confounds
-->be likened to "biases", and if so, do these "average out" in a manner which
-->can give us a useful mean or useful estimator?

I think that this is a very interesting point because, for averaging with
MSE optimization, it is possible to show using the strong law of large numbers
that the bias of the average estimator converges to the expected bias of any
individual estimator while the variance converges to zero.  Thus the only way
to cancel existing bias using averaging is to average two (or more) different
populations from two (or more) estimators which are (somehow) known to have
complementary bias.  The trick is of course the "somehow"... Any ideas?

-Michael
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Michael P. Perrone                                      Email: mpp at cns.brown.edu
Institute for Brain and Neural Systems                  Tel:   401-863-3920
Brown University                                        Fax:   401-863-3934
Providence, RI 02912