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ThrunGroup / FastForest

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Mse variance is wrongly calcualted #129

Open vxbrandon opened 2 years ago

vxbrandon commented 2 years ago

image

We use the variance of sample variance formula to find the variance of mse. And, here u4 indicates the fourth central moment of population, and currently we estimate it by the fourth central moment of sample. Yet, this estimation is biased, so we have to use another estimation that is unbiased. I'm gonna use h4 statistics, which is an unbiased estimation of u4.

Reference:

  1. https://en.wikipedia.org/wiki/Variance#Distribution_of_the_sample_variance
  2. https://www.mathstatica.com/book/Rose_and_Smith_2002edition_Chapter7.pdf#page=6
motiwari commented 2 years ago

Fixed?

vxbrandon commented 2 years ago

Fixed! But not sure that it's the right result!