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Desirable properties of estimators

Efficient Estimators. If unbias and has the smallest variance for given sample size, then most efficientHas smaller spread of valuesSample mean is more efficient than sample median as estimator of population meanSo a sample median is less likely than a sample mean to be a correct estimate of a po

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Desirable properties of estimators

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    1. Desirable properties of estimators Good estimators should be unbiased, efficient and consistent See chap 10 Keller Unbias => a sample statistic that, on average, across many samples, takes on value = population parameter Sample mean is always an unbiased estimator of population mean, similarly for sample proportions Sample Std Dev, s, is a biased estimate of population std dev ?

    2. Efficient Estimators If unbias and has the smallest variance for given sample size, then most efficient Has smaller spread of values Sample mean is more efficient than sample median as estimator of population mean So a sample median is less likely than a sample mean to be a correct estimate of a population mean

    3. Consistency A consistent estimator => the prob. that a sample statistic will be close to the population parameter approaches 1 as sample gets larger. Sample mean & sample proportion are consistent estimators of population mean & proportion respectively.

    4. Point Estimates Sample mean & sample proportion are used as unbiased, efficient & consistent estimators of ? and ? Especially when population normally distributed or large enough sample. If sample large can use sample variance to estimate population variance This is biased in small sample case Next look at estimates based on an interval rather than at a specific point.

    5. Confidence Intervals Aim to develop CI estimates for the mean & the proportion 2nd type of statistical inference CI => the estimate covers a range of values (an interval) rather than just a point estimate The interval will have a specified confidence or probability of correctly estimating the true value of the population parameter

    6. CI of Mean Depends on whether population variance is known or unknown If population has normal distribution or sample size large enough Then the 95% CI of population mean ? , with known Std Dev, is:

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