A point estimator is a statistic used to estimate the value of an unknown parameter of a population. Abbott 2. Should be unbiased. This is why the mean is a better estimator than the median when the data is normal (or approximately normal). Properties of Good Estimators ¥In the Frequentist world view parameters are Þxed, statistics are rv and vary from sample to sample (i.e., have an associated sampling distribution) ¥In theory, there are many potential estimators for a population parameter ¥What are characteristics of good estimators? The estimate is the numeric value taken by estimator. 2. These are: Unbiasedness; Efficiency; Consistency; Let’s now look at each property in detail: Unbiasedness. Is it normal to have the medicine come out your nose after a tonsillectomy? The bias of an estimator θˆ= t(X) of θ is bias(θˆ) = E{t(X)−θ}. population size, the estimator gets closer and closer to the Relative e ciency: If ^ 1 and ^ 2 are both unbiased estimators of a parameter we say that ^ 1 is relatively more e cient if var(^ 1)

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