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 ...
- No tags were found...
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Delta Method Cont<strong>in</strong>ues7 Compute derivative (gradient) of f: has components (1,−2x 2 ).Evaluate at y = (µ 2 +σ 2 ,µ) to geta t = (1,−2µ).This leads ton 1/2 (s 2 −σ 2 ) ≈ n 1/2 [1,−2µ][X 2 −(µ 2 +σ 2 )¯X −µ]which converges <strong>in</strong> distribution to(1,−2µ)MVN(0,Σ).This rv is N(0,a t Σa) = N(0,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 26 / 31