15
Aug
Unbiased Estimate Of Population Mean. An unbiased estimator is a statistic with an expected value that matches its corresponding population parameter. They may not be exactly correct because after all they are only an estimate but they have no systematic source of bias. The efficiency of the estimator under optimality compared with the mean per unit estimator an almost unbiased ratio estimator an unbiased product estimator and a regression estimator both. In fact every sample value is in itself an unbiased estimator of the population mean.
Introduction to the Science of Statistics Unbiased Estimation Example 142. Sometimes called a point estimator. In fact every sample value is in itself an unbiased estimator of the population mean. A statistic used to approximate a population parameter. Tin 1 suggested an almost unbiased ratio estimator estimate the population means. So it is desirable to construct unbiased estimators simultaneously keeping in mind its efficiency.
X X n X 1 X 2 X 3 X n n X 1 n X 2 n X 3 n X n n.
Show that the sample mean X is an unbiased estimator of the population mean μ. That is mathEX_i mu textfor all X_imathwhere mathmumath is the p. A statistic used to approximate a population parameter. Sometimes called a point estimator. Let X 1X 2X n be Bernoulli trials with success parameter p and set the estimator for p to be dXX the sample mean. Note that in this case the sample sum S n X 1 X 2.