STA261 Assignment 2
due: Wed.Mar.31/10
A sequence of statistical estimates
θ
n
with
n
∈
N
is said to be
consistent
for
the parameter
θ
i
ff
θ
n
d
→
θ
as
n
→ ∞
.
And any particular estimate
T
is said to be
unbiased
for
θ
i
ff
ET
=
θ
.
Thus, unbiasedness is about individual estimators, while consistency is
about sequences of such. Consistency is certainly the more fundamen
tal (and important) requirement that one would demand of an estima
tion procedure.
But it should be clear to the reader that given any
unbiased estimate,
T
, it would be extremely easy to construct a consis
tent sequence
θ
n
from a sample
T
1
, . . . , T
n
IID T
; this is because (by
any version of the law of large numbers) we need only take
θ
n
=
T
=
T
1
+
· · ·
+
T
n
n
.
And this is the chief merit of the property known as unbiasedness — that
it gives a quick and ready basis for the construction of consistent se
quences.
More important for any single estimate,
T
, than the property of unbi
asedness is just how close it actually is to the parameter,
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 Spring '10
 brenner
 Statistics, Standard Deviation, unbiased estimate, Unbiasedness

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