Department of Economics
Professor Dale J. Poirier
University of California, Irvine
December 5, 2006
FINAL
EXAM
ECON 220A
Statistics and Econometrics I
(open book)
Directions
: You must answer each of the following questions. Points (out of 100) are allocated
as noted to the left of each question. Allocate your time according to these points. To receive any
partial credit, you
must
show your work.
(20)
1.
Consider a random sample Y
t
(t = 1, 2, ..., T) from a N(
:
,
F
2
) distribution with unknown
mean and variance. Also consider the following loss function for estimating
F
2
:
Finally, consider estimators of the form
for some constant d, where S
2
is the
usual unbiased estimator of
F
2
. Find the value of d which minimizes risk.
(20)
2.
Consider a random sample Y
t
(t = 1, 2, ..., T) from the gamma distribution G(
"
,
$
). Find
a method of moments estimator of
"
and
$
.
3.
Suppose the opening prices per share X
1
and X
2
of two similar stocks are independent
random variables with common density f
X
(x) = ½ exp[-½(x-4)], 4 < x <

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