A point estimate is a single numerical value obtained using sample from the entire population that is used to approximate a parameter. The numerical value which is obtained using the sample values is called a statistic. For example to approximate the average height of all Americans we would take a random sample of some American and use the sample mean as a point estimate for the population mean.
Some examples of point estimates are sample mean which is used to approximate population mean, sample standard deviation which is used to approximate population standard deviation and sample proportion which is used to approximate population proportion.
A point estimate must have the following four characteristics to be a good estimate:
- Unbiasedness- This means that the mathematical expectation of the statistic must be equal to the parameter value.
- Consistency- This means that the statistic must converge in probability towards the actual parameter value as the sample size is made larger and larger.
- Efficiency- This means that the variance of the estimator must be as small as possible.
- Sufficiency- Roughly speaking this means that the estimator contains all the information in the sample regarding the parameter.
Some of the methods used to obtain point estimates are:
- Method of Maximum Likelihood estimates
- Method of Minimum Variance
- Method of Moments.
- Method of Least Squares.
- Method of Minimum Chi Square.
- Method of Inverse Probability.
