1
Large Sample Theory
Lecture XIV
I.
Basic Sample Theory
A.
The problems set up is that we want to discuss sample theory.
1.
First assume that we want to make an inference, either estimation
or some test, based on a sample.
2.
We are interested in how well parameters or statistics based on that
sample represent the parameters or statistics of the whole
population.
B.
The complete statistical term is known as convergence.
1.
Specifically, we are interested in whether or not the statistics
calculated on the sample converge toward the population
estimates.
2.
Let
n
X
be a sequence of samples.
We want to demonstrate that
statistics based on
n
X
converge toward the population statistics
for
X
.
C.
Taking a slightly different tack:
The classical assumptions for ordinary
least squares (OLS) as presented in White, Halbert Asymptotic Theory for
Econometricians.
1.
Theorem 1.1: The following are the assumptions of the classical
linear model:
a)
The model is known to be
,
y
X
.
b)
X
is a nonstochastic and finite
n
k
matrix.
c)
X X
is nonsingular for all
n
k
.
d)
0
E
.
e)
2
2
0
0
~
0,
,
N
I
.
2.
Given these assumptions, we can conclude that
a)
(Existence) Given (i.)(iii.),
n
exists for all
n
k
and is
unique.
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 Fall '09
 CARRIKER
 Normal Distribution, Standard Deviation, Probability theory, Classical Linear Model, Charles B. Moss

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