Information Technology Reference
In-Depth Information
a
()()
qgz
F
z
.
n
,
n
n
But
q
n
,a
= ar
n
+
o
(
n
) and
z
n
Æ l. So the last display is, up to
o
(
n
),
ng
()
=
()
ar
l a
g
l r
.
Likewise, the conditional variance of S
i
=1
Y
i
2
is
q
n
,a
{2 + n(
z
n
)} =
O
(
n
); the
conditional standard deviation is
O
(
n
). Thus
q
Â
=
()
+
()
Y
i
2
g
lr
no n
,
i
=
n
1
Â
=
()
+
()
2
Y
g
la ,
o
1
i
q
i
=
1
-
()
-
n
1
1
g
lr
ar
Â
Y
+
()
2
=
o
1
.
i
nq
-
1
iq
=+
1
This completes the argument for the convergence in probability. The
assertion about the
t
statistic is easy to check, using the last display.
REFERENCES
Diaconis P; Freedman D. “On the Maximum Difference Between the Empirical
and Expected Histograms for Sums,”
Pacific Journal of Mathematics
, 1982;
100
:287-327.
Freedman D. “Some Pitfalls in Large-Scale Econometric Models: A Case Study,”
University of Chicago Journal of Business
, 1981;
54
:479-500.
Freedman D; Rothenberg T; Sutch R. “A Review of a Residential Energy End Use
Model,” Technical Report No. 14, University of California, Berkeley, Dept. of
Statistics, 1982.
—— “On Energy Policy Models,”
Journal of Business and Economic Statistics
,
1983;
1
:24-32.
Judge G; Bock M.
The Statistical Implications of Pre-Test and Stein-Rule Estimators
in Econometrics
, Amsterdam: North-Holland, 1978.
Kendall MG; Stuart A.
The Advanced Theory of Statistics
, London: Griffin, 1969.
Olshen RA. “The Conditional Level of the
F
-Test,”
Journal of the American
Statistical Association
, 1973;
68
, 692-698.
Rencher AC; Pun FC. “Inflation of
R
2
in Best Subsets Regression,”
Technometrics
,
1980;
22
:49-53.
