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# notes509fall11sec41 - STAT 509 Section 4.1 Estimation...

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STAT 509 – Section 4.1 – Estimation Parameter : A numerical characteristic of a population. Examples: Statistic : A quantity that we can calculate from sample data that summarizes a characteristic of that sample. Examples: Point Estimator : A statistic which is a single number meant to estimate a parameter. It would be nice if the average value of the estimator (over repeated sampling) equaled the target parameter. An estimator is called unbiased if the mean of its sampling distribution is equal to the parameter being estimated. Examples:

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we want it to be as precise as possible. The standard deviation of a statistic’s sampling distribution is called the standard error of the statistic. The standard error of the sample mean Y is n / . Note: As the sample size gets larger, the spread of the sampling distribution gets smaller. When the sample size is large, the sample mean varies less across samples. Evaluating an estimator : (1) Is it unbiased? (2)
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notes509fall11sec41 - STAT 509 Section 4.1 Estimation...

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