Unformatted text preview: ε i are iid measurement errors with zero mean and common variance σ 2 , use conditional SM analysis to find the variance of (XZ ,…,Z ). Plot this ε 1 n conditional variance against n for σ 2 = 1 and σ 2 either 1 or 0.2. ε Useful result on the inverse of covariance matrices with a special “equicorrelated” structure. The inverse of an n × n matrix A of the type: ρ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎡ 1 1 ρ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ A σ = 2 is: ] ⎡ [1 ρ + ρ − + ] [1 ] ) 2 n ( −ρ −ρ 2) (n ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 1 − A σ = 2 (1 ρ − 1 )[ + ( n − 1) ρ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 1...
View
Full Document
 Spring '05
 DanieleVeneziano
 Variance, Probability theory, supermarket chain, ρij, conditional SM analysis

Click to edit the document details