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Topic: i.i.d order statistics and extreme value theory - advice on where
asymptotic normal ends and nonnormal limiting distributions begin

Replies: 2   Last Post: Dec 31, 2011 6:30 PM

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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
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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 extreme-value 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 m-th-extreme, 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.




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