The ENTROPY Procedure (Experimental)
- Overview
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Getting Started
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Syntax
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DetailsGeneralized Maximum EntropyGeneralized Cross EntropyMoment Generalized Maximum EntropyMaximum Entropy-Based Seemingly Unrelated RegressionGeneralized Maximum Entropy for Multinomial Discrete Choice ModelsCensored or Truncated Dependent VariablesInformation MeasuresParameter Covariance For GCEParameter Covariance For GCE-MStatistical TestsMissing ValuesInput Data SetsOutput Data SetsODS Table NamesODS Graphics
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Examples
- References
Parameter Covariance For GCE
For the cross-entropy problem, the estimate of the asymptotic variance of the signal parameter is given by:
![\[ \hat{Var}(\hat{\beta })=\frac{\hat{\sigma _{\gamma }^{2}}(\hat{\beta })}{\hat{\psi ^{2}}(\hat{\beta })}(X’X)^{-1} \]](images/etsug_entropy0192.png){kind=small} |
where
![\[ \hat{\sigma _{\gamma }^{2}}(\hat{\beta })=\frac{1}{N}\sum _{i=1}^{N}\gamma _{i}^{2} \]](images/etsug_entropy0193.png){kind=small} |
and 
is the Lagrange multiplier associated with the i th row of the 
constraint matrix. Also,
![\[ \hat{\psi ^{2}}(\hat{\beta })=\left[ \frac{1}{N}\sum _{i=1}^{N}\left( \sum _{j=1}^{J}v_{ij}^{2}w_{ij} -(\sum _{j=1}^{J}v_{ij}w_{ij})^{2} \right) ^{-1} \right]^{2} \]](images/etsug_entropy0196.png) |