STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...

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First graphN(0,1/n) vs X=0; n=100000.0 0.2 0.4 0.6 0.8 1.0X=0N(0,1/n)••-3 -2 -1 0 1 2 3N(0,1/n) vs X=0; n=100000.0 0.2 0.4 0.6 0.8 1.0X=0N(0,1/n)••-0.03 -0.02 -0.01 0.0 0.01 0.02 0.03Richard Lockhart (Simon Fraser University) STAT 830 Convergence in Distribution STAT 830 — Fall 2011 8 / 31
Second graphN(1/n,1/n) vs N(0,1/n); n=100000.0 0.2 0.4 0.6 0.8 1.0N(0,1/n)N(1/n,1/n)•• ••••••••••••••••-3 -2 -1 0 1 2 3N(1/n,1/n) vs N(0,1/n); n=100000.0 0.2 0.4 0.6 0.8 1.0N(0,1/n)N(1/n,1/n)•-0.03 -0.02 -0.01 0.0 0.01 0.02 0.03Richard Lockhart (Simon Fraser University) STAT 830 Convergence in Distribution STAT 830 — Fall 2011 9 / 31
Page 1 and 2: STAT 830Convergence in Distribution
Page 3 and 4: Convergence in Distribution p 72Und
Page 5 and 6: Some numerical examples?Answers dep
Page 7: Answering the questionsX n ∼ N(0,
Page 11 and 12: Third graphN(1/sqrt(n),1/n) vs N(0,
Page 13 and 14: The Central Limit Theorem pp 77-79T
Page 15 and 16: Edgeworth expansionsIn fact if γ =
Page 17 and 18: RemarksThe error using the central
Page 19 and 20: Extensions of the CLT1 Y 1 ,Y 2 ,·
Page 21 and 22: The delta method pp 79-80, 131-135T
Page 23 and 24: How to apply δ method1 Write stati
Page 25 and 26: Delta Method ContinuesUsing binomia
Page 27 and 28: Alternative approachSuppose c is co
Page 29 and 30: Example - medianMany, many statisti
Page 31: MedianIf we put x = m+y/ √ n (whe

STAT 830 Convergence in Distribution - People.stat.sfu.ca - Simon ...

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