A good estimator is one which is as close to the true value of the parameter as possible.
The properties of a good estimator for evaluating sample statistics are:
Unbiasedness:
A good estimator is unbiased, meaning the expected value of the estimator is equal to the true population parameter.
Consistency:
A good estimator exhibits consistency, meaning as the sample size increases towards infinity, the estimates converge closer and closer to the true population parameter with probability 1.
• In simpler terms, the more data you have (larger sample size), the more confident you can be that your estimate reflects the actual population value.
Efficiency:
Among unbiased estimators, the one with the smallest variance is considered the most efficient. Variance measures how spread out the estimates are around the true value. A good estimator has low variance, indicating the estimates are clustered closer to the true parameter, leading to more precise estimations.
Sufficiency:
A good estimator is sufficient if it captures all the relevant information in the sample that is necessary to estimate the population parameter.
