A Weighted Generalized Maximum Entropy Estimator with a Data-driven Weight

The method of Generalized Maximum Entropy (GME), proposed in Golan, Judge and Miller (1996), is an information-theoretic approach that is robust to multicolinearity problem. It uses an objective function that is the sum of the entropies for coefficient distributions and disturbance distributions. This method can be generalized to the weighted GME (W-GME), where different weights are assigned to the two entropies in the objective function. We propose a data-driven method to select the weights in the entropy objective function. We use the least squares cross validation to derive the optimal weights. Monte Carlo simulations demonstrate that the proposed W-GME estimator is comparable to and often outperforms the conventional GME estimator, which places equal weights on the entropies of coefficient and disturbance distributions.