Tuesday, February 7, 2012

On the Asymptotic Properties of Sample Means

Last month, in a post titled "Extracting the Correct Mean(ing) From the Data" (here), I discussed some aspects of the arithmetic, geometric, and harmonic sample means.

In a subsequent comment, I was asked if the geometric mean (GM) and harmonic mean (HM) are consistent estimators of E[X], the (arithmetic) mean of the population. My first reaction was that they are, but a little further reflection shows otherwise.