Class Notes in Statistics and Econometrics Part 34 pps
Class Notes in Statistics and Econometrics Part 34 pps
... back, and you regress y on X with a constant term. (The under-
lining does not denote taking out of the mean, but the taking out of the seasonal
means and adding back of the overall mean.) In the ... causality should be included in
statistics textbooks.
Innovation accounting or impulse response functions: make a moving average
representation, and then you can pick the timepath of...
Class Notes in Statistics and Econometrics Part 4 pps
... argument
inside.
220 8. VECTOR RANDOM VARIABLES
1), and if cov[x, y] = 0, then x and y are independent. (I.e., in this respect indicator
variables have similar properties as jointly normal random ... independent.
Problem 136. If the vector random variables x and y have the property that
x
i
is independent of every y
j
for all i and j, does that make x and y independent
random ve...
Class Notes in Statistics and Econometrics Part 5 pps
... the inner integral becomes −
1
2π
e
−t
∞
0
=
1
2π
; therefore the whole integral is 1. Therefore the product of the integrals of the
marginal densities is 1, and since each such marginal integral ... First
we will introduce the multivariate standard normal, which one obtains by applying
only operations (1) and (2), i.e., it is a vector composed of independent univariate
standard norma...
Class Notes in Statistics and Econometrics Part 12 ppsx
... lefthand side; it is amazing and surprising that it is exactly the population
equivalent of the F -test for testing α = 0 in the regression with intercept. It can be estimated by
replacing α
2
with ... the
following:
Theorem 24.2.2.
ˆ
β is a linear minimax est imator of the parameter vector β
in the following sense: for every nonrandom coefficient vector t, t
ˆ
β is the linear
640 24. S...
Class Notes in Statistics and Econometrics Part 13 pps
... linear
in P y are also linear in y and vice versa,
ˆ
β is also the BLUE in the original GLS
model.
Problem 319. 2 points Show that
(26.0.3)
ˆ
β −β = (X
Ψ
−1
X)
−1
X
Ψ
−1
ε
ε
ε
and derive from this ... than those familiar from linear estimators. The problem at hand can be
reduced to a minimum trace problem as defined in Rao [Rao73, pp. 65–66], and
part of the following proof...
Class Notes in Statistics and Econometrics Part 14 ppsx
... best linear bounded MSE predictor of z based on y, µ, and ν.
• a. Give special cases of this specification in which µ and ν are constant and y
and z random, and one in which µ and ν and y are random ... are random and z is constant, and
one in which µ and ν are random and y and z are constant.
27.1. MINIMUM MEAN SQUARED ERROR, UNBIASEDNESS NOT REQUIRED 713
informa...
Class Notes in Statistics and Econometrics Part 17 pps
... within-group or between-group phenomena or both.:
• negative relationship of protein % and oil % (both within • and ◦);
• p osit ive relationship of oil % and seed size (both within • and ◦ and ... of seed size and height;
• p osit ive relationship of height and lodging (within ◦ and between groups);
• negative relationship of oil % and lodging (between groups and possibly...
Class Notes in Statistics and Econometrics Part 18 pps
... do something which he do e s not quite understand is in the above eliciation of
prior information. It often happens that prior information gained in this way is self-
contradictory, and the researcher ... and variance alone.
Problem 395. 4 points Show that, if y is normally distributed, s
2
and
ˆ
β are
independent.
Answer. We showed in question 300 that
ˆ
β and ˆε are uncorrelat...
Class Notes in Statistics and Econometrics Part 20 pps
... Scenario: Minimizing relative increase in Mahalanobis
distance i f distribution is known
We start with a situation where the e xpec ted values of the random vectors y and
z are known, and their joint ... minimize the relative increase in the Maha-
lanobis distance (instead of selecting its minimax value) because all parameters of
the underlying distribution were known. The simplest si...
Class Notes in Statistics and Econometrics Part 29 ppsx
... u
t
is independent of ε
s−1
. Since s < t, therefore in particular s = t, u
t
is also independent of
u
s
. Therefore u
t
is independent of any function of ε
s−1
and u
s
, in particular, it is independent ... process independent of the pre-sample disturbance
ε
0
, and α
0
> 0 and 0 < α
1
< 1 are two constants.
• a. 2 points Show that u
t
is independent of all ε
s
with 0...