A Proof for Lehmann-Sche↵e Theorem Kun Meng
[email protected] Department of Biostatistics Brown University, Providence, RI, 02903, USA
Lehmann-Sche↵e Theorem: Suppose that P is a family of populations, T is a sufficient and complete statistic for P, and ✓ is an estimable parameter functional on P. If S is an unbiased estimator of ✓, then EP (S|T ), which does not depend on the choice of P 2 P, is the unique UMVUE of ✓.
1
for
A
Lehmann
proof
( the
is
-
also
Swheffe
theorem
'
the
estimable
$
7-
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for
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.
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.
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for
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Van
with
,
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implies
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e
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of
-
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-
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for
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=
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.
.
,