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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How to apply δ method1 Write <strong>stat</strong>istic as a function of averages:◮ Def<strong>in</strong>eW i =[ ]X2i.X i◮ See that [X2¯W n =]X◮ Def<strong>in</strong>ef(x 1 ,x 2 ) = x 1 −x 2 2◮ See that s 2 = f( ¯W n ).2 Compute mean of your averages:[ ] [µ W ≡ E( ¯W E(X2n ) = i) µ=2 +σ 2E(X i ) µ].3 In δ method theorem take Y n = ¯W n and y = E(Y n ).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 23 / 31
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