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« **on:** October 18, 2011, 04:22:49 PM »
If the mean value of an estimator equals the true value of the quantity it estimates, then the estimator is called an unbiased estimator. For example, assume that the sample mean is being used to estimate the mean of a population. Using the Central Limit Theorem, the mean value of the sample means equals the population mean. Therefore, the sample mean is an unbiased estimator of the population mean.

If the mean value of an estimator is either less than or greater than the true value of the quantity it estimates, then the estimator is called a biased. For example, suppose you decide to choose the smallest observation in a sample to be the estimator of the population mean. Such an estimator would be biased because the average of the values of this estimator would always be less than the true population mean. In other words, the mean of the sampling distribution of this estimator would be less than the true value of the population mean it is trying to estimate. Consequently, the estimator is a biased estimator.

Above is just introduction part. I want to know more about it..such as at what places which one is preferred. What are advantages and disadvantages. Anything related to the topic is welcome.. Lets start the Discussion.