STAT 509 – Section 4.1 – Estimation
Parameter
:
A numerical characteristic of a population.
Examples:
Statistic
:
A quantity that we can calculate from sample
data that summarizes a characteristic of that sample.
Examples:
Point Estimator
:
A statistic which is a single number
meant to estimate a parameter.
It would be nice if the average value of the estimator
(over repeated sampling) equaled the target parameter.
An estimator is called unbiased
if the mean of its
sampling distribution is equal to the parameter being
estimated.
Examples:
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we want it to be
as
precise
as possible.
The standard deviation of a statistic’s sampling
distribution is called the standard error
of the statistic.
The standard error of the sample mean Y
is
n
/
.
Note:
As the sample size gets larger, the spread of the
sampling distribution gets smaller.
When the sample size is large, the sample mean varies
less
across samples.
Evaluating an estimator
:
(1)
Is it unbiased?
(2)
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 Fall '08
 CHALMERS
 Normal Distribution

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