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There are four main properties associated with a "good" estimator. These are:
1) Unbiasedness: the expected value of the estimator (or the mean of the estimator) is simply the figure being estimated. In statistical terms, E(estimate of Y) = Y.
2) Consistency: the estimator converges in probability with the estimated figure. In other words, as the sample size approaches the population size, the estimator gets closer and closer to the estimated.
3) Efficiency: The estimator has a low variance, usually relative to other estimators, which is called relative efficiency. Otherwise, the variance of the estimator is minimized.
4) Robustness: The mean-squared errors of the estimator are minimized relative to other estimators.
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