Marc Raimondo - CMI
Marc Raimondo - CMI
Marc Raimondo - CMI
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The Tracy-Widom approximation<br />
Let W = logit(x1) = log(x1/(1 − x1)).<br />
Result: [IMJ] As p ∝ n1,n2 → ∞, (and with O(p −2/3 ) error):<br />
In other words:<br />
Percentiles fα:<br />
f.90 = 0.4501<br />
f.95 = 0.9793<br />
f.99 = 2.0234<br />
W − µp<br />
σp<br />
D<br />
⇒ W∞ ∼ F1.<br />
x1 ≈ eµ+σW∞<br />
. µ+σW∞ 1 + e<br />
0.3<br />
0.25<br />
0.2<br />
0.15<br />
0.1<br />
0.05<br />
-4 -2 2 4<br />
Luminy 12/08 – p.23
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