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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The delta method pp 79-80, 131–135TheoremSuppose:Sequence Y n of rvs converges to some y, a constant.X n = a n (Y n −y) then X n converges <strong>in</strong> distribution to some randomvariable X.f is differentiable ftn on range of Y n .Then a n (f(Y n )−f(y)) converges <strong>in</strong> distribution to f ′ (y)X.If X n ∈ R p and f : R p ↦→ R q then f ′ is q ×p matrix of first derivatives ofcomponents of f.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 21 / 31