Error in Lack of Correlation Assumption

• If ,
• then ,
• and all one can say in general is that

  

• The uncorrelated estimate is

  

• and the true satisfies

  

• where extremes are only attained when which is a most dangerous case.

• Other ratios, are better, e.g., !

• For n variables, all one can say rigorously is

  

  which is clearly pretty bad for large n.