Approach to estimating other parameters
In the previous section, we described standard errors and confidence intervals
for sample means. Population means are the most commonly estimated parameters,
but there are many applications where other parameters are of greater interest.
The approach is similar.
- Point estimate
- To estimate a population parameter, the corresponding sample statistics
is used.
- Error distribution
- The estimate is unlikely to be equal to the population parameter. The
estimation error has a distribution.
- Standard error and bias
- A good estimator usually has an error distribution whose mean is zero
(unbiased). The standard deviation of the error distribution is called the
standard error. The standard error may depend on unknown parameters.
- From data:
- We can usually find a numerical value for the standard error (or an approximation
to it). The standard error tells you how far the estimate is likely to be
from the population parameter.