Econometrics 10
1.1.
var(
) is inversely proportional to
n
1.1.1.
the spread (standard deviation) of the sampling
distribution is proportional to 1/
1.1.2.
Thus the sampling uncertainty associated with
is
proportional to 1/
(larger samples, less uncertainty, but square
root law)
•
The sampling distribution of
when
n
is large (note 133)
For small sample sizes, the distribution of
will usually be complicated (
unless
. . .
what is true
about the distribution of the Y
i
values in the population?)
But if
n
is large, the sampling distribution is simple!
1.1.
As
n
increases, the distribution of
becomes more tightly centered
around
μ
Y
(the
Law of Large Numbers
)
1.2.
Moreover, the distribution of
both
become normal (the
Central
Limit Theorem
)
1.2.1.
1.2.2.
•
The
Law of Large Numbers
: (note 134)
An estimator is
consistent
if the probability that its falls within an interval of the true population
value tends to one as the sample size increases.
If (
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 Winter '12
 Simpson
 Econometrics, Normal Distribution, Standard Deviation, µY

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