Estimators

An estimator is a guess of a population parameter based on a sample data.

Process of Estimation

Estimating a population parameter from a sample data.

Unbiasedness

If a statistic is used as an estimator for population parameter and , then it is said to be an unbiased estimator of .

Types

Point estimator

A statistics which can be used to get a single number as the result. The estimated value can be considered as the most plausible value of a parameter.

Interval estimator

A statistics which can give an upper limit and a lower limit calculation based on the point estimator. A pair of values calculated as the upper and the lower limits for a population parameter.

Accuracy

Mean, variance, standard deviation can be estimated with a sample.

Sample mean is an unbiased estimator for a continuous random variable. Aka. best linear unbiased estimator (BLUE).

Sample variance is an unbiased estimator.

Note

Sample variance can be estimated using: