A numerical measure of the reliability of the

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Unformatted text preview: measure of the reliability of the estimation: the error in the estimation Estimator: Definition An estimator is a rule or a mathematical formula that tells us how to calculate the estimate based on the sample Point estimator : A single number is calculated from the sample to estimate the parameter Interval estimator : Two numbers are given such that the interval between these two numbers contain the parameter with a high (pre-specified) probability Properties of Point Estimators Since an estimator is calculated from sample values, it varies from sample to sample according to its sampling distribution An estimator is unbiased if the mean of its sampling distribution equals the parameter of interest Such an estimator does not systematically underestimate or overestimate the parameter the sample mean is an unbiased estimator of the population mean; the sample proportion is an unbiased estimator of the population proportion Properties of Point Estimators (Cont.) Among unbiased estimators of a parameter, we prefer the ones whose sampling distributions have smaller spread or variability...
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