Estimators
Broadly, an estimator is a
mathematical function that approximates a population parameter
depending only on sample information.
Examples of estimators
and the corresponding parameters:
. Bias
The expected value of an unbiased estimator is the
population parameter. The bias in this case
is 0. If the expected
value of an
estimator is (parameter + b), then the bias is b.
. Efficiency
The
most efficient estimator is the one
with the smallest variance.
Estimates
An estimate is the output that you
get from the estimator (when you
apply the formula). There are two
types
of estimates: point estimates and
confidence interval estimates
Point estimates- A single
value. Examples: • 1
• 5
• 122.67
• 0.32
Confidence estimates - An interval. Examples:
•
( 1 , 5 )
•
( 12 , 33)
•
( 221.78
, 745.66)
.( - 0.71 , 0.11)
Confidence intervals
are much more precise than point estimates. That
is why they are preferred when making
inferences
