jdm
Posts:
16
Registered:
11/22/10


i.i.d order statistics and extreme value theory  advice on where asymptotic normal ends and nonnormal limiting distributions begin
Posted:
Dec 30, 2011 3:30 PM


I've been studying some cryptographic research in which the asymptotic normal distribution of the empirical sample quartile of order q is used to construct statistical models of the amount of data required for a successful cryptanalysis.
The main issue I have is that, while I'm pretty sure that such models have continued to be used for order statistics X_i (with i near to n) where the asymptotic normal distribution is inaccurate and where something based on extremevalue theory for the mth extremes would have been better, I don't have any idea as to how to compute an estimate for the value of i (or indeed q) above which the asymptotic normal might be considered suspect.
As an example, I'm currently dealing with the situation X_1 <= X_2 ...<= X_n, where n = 2^{41}1 = 2,199,023,255,551. In particular, I'm trying to work out whether the asymptotic normal is likely to be adequate when drawing conclusions about the top 2^{17} = 131,072 values or not  and while this seems a high m for mthextreme, it's not so high in relation to n, and this would mean I was dealing with the top 0.000006388% of values.
Can anyone give me some advice here?
Many thanks,
James McLaughlin.

