Bias of An Estimator - Effect of Transformations

Effect of Transformations

Note that, when a transformation is applied to a mean-unbiased estimator, the result need not be a mean-unbiased estimator of its corresponding population statistic. That is, for a non-linear function f and a mean-unbiased estimator U of a parameter p, the composite estimator f(U) need not be a mean-unbiased estimator of f(p). For example, the square root of the unbiased estimator of the population variance is not a mean-unbiased estimator of the population standard deviation.