2014 Econ 2040 Final Solutions
Question 1
Using = we can write:
= + = + = +
where = + . We then have
=
1
= +
X
=1
1
X
!1
1
=1
X
!1
=1
1
!
X
=
=1
1
!
X
=1
!1
1
X
1
+
=1
X
=1
!
We then need to show that [ ] = 0:
[( + ) ( + )] = [ ] + [
1
Verifying stochastic equicontinuity for a rst-step kernel density
estimator
In the case of kernel estimators, stochastic equicontinuity is veried using so-called U -statistics. The idea is
that
n
h
i
X
n1/2
D zi , h h0 E D zi , h h0 |h
i=1
can be wri
Econ 2040
Spring 2014
Problem Set 4
1) Suppose that is distributed as ( 0 0 ), where
1 if 0
( ) =
0
if 0
and where (0 0 ) is known to lie in [01 10] [01 10]. Assume that we have access to an
iid sample (1 ).
. (Hint: it may not
a) Find the maximum likel
Econ 2040
Problem Set 3
Question 1. Consider the regression model:
y i xi i ,
in which x i and y i are scalar, i 1,2,.n , with x i 0 for all i,
and E i | x i 0 , Var i | x i 2 x i , where x i 0 , 1 1 and E i j | x 0
for all i and j. For example, we might
PS 2 due Th 2/27
1. Let Xi be an iid sequence of random scalars, with Xi ~ N(0,1).
n
If
2X
n
i 1
n
X
i 1
i
d Y , what is the distribution of Y?
2
i
2. Suppose that the model is
y t x t t , t 1,2,.T
but the econometrician mistakenly postulates:
y t x t z
Econ 2040 Midterm, Fall 2014, Solutions
Question 1)
1.1 b)
1.2 c)
1.3 d)
1.4 c)
Question 2)
a. Which restricted and unrestricted regressions do you need to run in order to test each of the following 3
joint restrictions:
The unrestricted one is always the
Problem Set 1
Due: Tues, Feb 11th 2014
Question 1. A physicist makes 25 independent measurements of the specific gravity of a certain
body. He knows that the limitations of his equipment are such that the standard deviation of each
measurement is units.
a
Problem Set 5
Do not hand in.
Question 1. We wish to estimate the coecients 1 and 2 in the model:
= 1 1 + 2 2 +
(1)
in which the variable 1 is correlated with and, furthermore, the error term is known to be heteroskedastic of the form
Var [ ] = 2 2
(2)