STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...
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Edgeworth expansionsIn fact if γ = E(X 3 ) thenφ(t) ≈ 1−t 2 /2−iγt 3 /6+···keep<strong>in</strong>g one more term.Thenlog(φ(t)) = log(1+u)whereu = −t 2 /2−iγt 3 /6+··· .Use log(1+u) = u −u 2 /2+··· to getlog(φ(t)) ≈ [−t 2 /2−iγt 3 /6+···]−[···] 2 /2+···which rearranged islog(φ(t)) ≈ −t 2 /2−iγt 3 /6+··· .Richard Lockhart (<strong>Simon</strong> Fraser University) <strong>STAT</strong> <strong>830</strong> <strong>Convergence</strong> <strong>in</strong> <strong>Distribution</strong> <strong>STAT</strong> <strong>830</strong> — Fall 2011 15 / 31
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