Friday, December 27, 2013

Unbiased Estimation of a Standard Deviation

Frequently, we're interested in using sample data to obtain an unbiased estimator of a population variance. We do this by using the sample variance, with the appropriate correction for the degrees of freedom. Similarly, in the context of a linear regression model, we use the sum of the squared OLS residuals, divided by the degrees of freedom, to get an unbiased estimator of the variance of the model's error term.

But what if we want an unbiased estimator of the population standard deviation, rather than the variance?