Why is s a biased estimator

Active 4 years, 10 months ago. Viewed 2k times. Add a comment. Active Oldest Votes. I may be completely misunderstanding though. Note that the cross-product term term vanishes and Expectation of a constant is the same constant. I see your contemporaneous Answ. Great minds An estimator of a given parameter is said to be consistent if it converges in probability to the true value of the parameter as the sample size tends to infinity.

Common Approach for finding sub-optimal Estimator: Restrict the estimator to be linear in data. Find the linear estimator that is unbiased and has minimum variance. If one or more of the estimators are biased, it may be harder to choose between them. For example, one estimator may have a very small bias and a small variance, while another is unbiased but has a very large variance.

In this case, you may prefer the biased estimator over the unbiased one. The sample proportion, P is an unbiased estimator of the population proportion,. Unbiased estimators determines the tendency , on the average, for the statistics to assume values closed to the parameter of interest. Without evaluating the whole population, the population parameter can be computed with accuracy based on the unbiased estimator from a sample drawn from the population. This is because in repeated sampling, the unbiased estimator results in an average value that is equal to the parameter itself.

Therefore, the sample mean is an unbiased estimator of the population mean. Ask Question. Asked 10 years, 4 months ago. Active 3 months ago. Viewed 66k times. Improve this question. Dav Weps Dav Weps 1 1 gold badge 6 6 silver badges 3 3 bronze badges. Add a comment. Active Oldest Votes.

Improve this answer. Macro Macro List of Partners vendors. Share Flipboard Email. Courtney Taylor. Professor of Mathematics. Courtney K. Taylor, Ph.

Updated January 13, Cite this Article Format. Taylor, Courtney. Unbiased and Biased Estimators. Functions with the T-Distribution in Excel.

Explore Maximum Likelihood Estimation Examples. Calculating a Confidence Interval for a Mean.