A question on X validated led me to wonder at the point made by Christopher Bishop in his Pattern Recognition and Machine Learning book about the MLE of the Normal variance being biased. As it is illustrated by the above graph that opposes the true and green distribution of the data (made of two points) […]
Category: bias
More on Bias Corrected Standard Deviation Estimates
This note is just a quick follow-up to our last note on correcting the bias in estimated standard deviations for binomial experiments. For normal deviates there is, of course, a well know scaling correction that returns an unbiased estimate for observed standard deviations. It (from the same source): … provides an example where imposing the … Continue reading More on Bias Corrected Standard Deviation Estimates
How to de-Bias Standard Deviation Estimates
This note is about attempting to remove the bias brought in by using sample standard deviation estimates to estimate an unknown true standard deviation of a population. We establish there is a bias, concentrate on why it is not important to remove it for reasonable sized samples, and (despite that) give a very complete bias … Continue reading How to de-Bias Standard Deviation Estimates