The ENTROPY Procedure (Experimental)

Parameter Covariance For GCE

For the cross-entropy problem, the estimate of the asymptotic variance of the signal parameter is given by:

\[ \hat{Var}(\hat{\beta })=\frac{\hat{\sigma _{\gamma }^{2}}(\hat{\beta })}{\hat{\psi ^{2}}(\hat{\beta })}(X’X)^{-1} \]

where

\[ \hat{\sigma _{\gamma }^{2}}(\hat{\beta })=\frac{1}{N}\sum _{i=1}^{N}\gamma _{i}^{2} \]

and $\gamma _{i}$ is the Lagrange multiplier associated with the i th row of the $Vw$ constraint matrix. Also,

\[ \hat{\psi ^{2}}(\hat{\beta })=\left[ \frac{1}{N}\sum _{i=1}^{N}\left( \sum _{j=1}^{J}v_{ij}^{2}w_{ij} -(\sum _{j=1}^{J}v_{ij}w_{ij})^{2} \right) ^{-1} \right]^{2} \]