Defnition oF Estimator and Choosing among
Estimators: Lecture XVII
Charles B. Moss
October 9, 2010
I. What is an Estimator?
A. In the next several lectures we will be discussing statistical esti
mators and estimation. The book divides this discussion into the
estimation of a single number such as a mean or standard devia
tion or the estimation of a range such as a conFdence interval.
B. At the most basic level, the deFnition of an estimator involves the
distinction between a sample and a population.
1. In general we assume that we have a random variable (
X
)
with some distribution function.
2. Next, we assume that we want to estimate something about
that population, for example we may be interested in esti
mating the mean of the population or probability that the
outcome will lie between two numbers.
a) ±or example, in a farmplanning model we may be inter
ested in estimating the expected return for a particular
crop.
b) In a regression context, we may be interested in estimating
the average e²ect of price or income on the quantity of
goods consumed.
3. This estimation is typically based on a sample of outcomes
drawn from the population instead of the population itself.
C. Common point estimators are the sample moments
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentAEB 6571 Econometric Methods I
Professor Charles B. Moss
Lecture XVII
Fall 2010
1. Sample Mean
¯
X
=
1
n
n
X
i
=1
X
i
(1)
2. Sample Variance
S
2
X
=
1
n
n
X
i
=1
±
X
t
−
¯
X
²
2
=
1
n
n
X
i
=1
X
2
t
−
±
¯
X
²
2
(2)
3. The
k
th
sample moment around zero
M
k
=
1
n
n
X
i
=1
X
k
i
(3)
4.Th
e
k
th
moment around the mean
˜
M
k
=
1
n
n
X
i
=1
±
X
i
−
¯
X
²
k
(4)
5. Sample Covariance
Cov (
X,Y
)=
S
xy
=
1
n
n
X
i
=1
±
X
i
−
¯
X
²±
Y
i
−
¯
Y
²
(5)
6. Sample Correlation
ρ
xy
=
S
xy
S
xx
S
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 Staff
 Probability theory, Cumulative distribution function, Professor Charles, Professor Charles B. Moss, Lecture XVII

Click to edit the document details