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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Alternative approachSuppose c is constant. Def<strong>in</strong>e Xi ∗ = X i −c.Sample variance of Xi ∗ is same as sample variance of X i .All central moments of Xi ∗ same as for X i so no loss <strong>in</strong> µ = 0.In this <strong>ca</strong>se:[a t µ4 −σ= (1,0) Σ =4 ]µ 3µ 3 σ 2 .Notice thata t Σ = [µ 4 −σ 4 ,µ 3 ] a t Σa = µ 4 −σ 4 .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 27 / 31