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Unformatted text preview: Chapter 7.1 : Point Estimation Point estimate Properties of Estimators The primary aim of statistical inference is to draw some conclusions about the unknown parameter , say, mean or variance. Point estimation deals with methods to come up with a single value, based on the observed data. Let the rv X follow )  ( or )  ( x f x p where is the unknown parameter. Definition : A point estimate of a population parameter is a single number calculated from sample data. The statistic used to calculate an estimate is called an estimator and denoted by . Some examples are given in the table below: characteristic Population Parameter Sample Estimator Proportion p Mean x Standard Deviation S 1 An estimator is unbiased if in repeated random samples the numerical values are grouped around ; that is, if the mean value of . ) ( = = E The difference between the mean of and is called the bias. That is, bias of  = . ) ( E = Example 1 : Sample mean  x is an unbiased estimator of the population mean , because x = Sample proportion p is an unbiased estimator of the population proportion , because p = . Definition . An estimator is consistent if ] [ P 0, as n . Result : If n as 0, ) ( SE , then the estimator is consistent. Example 2 : 2 (i) Note x is consistent, because its SE ) / ( = n x , as n ....
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This note was uploaded on 07/25/2008 for the course STT 351 taught by Professor Palaniappan during the Summer '08 term at Michigan State University.
 Summer '08
 Palaniappan

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