Partially adaptive estimation via the maximum entropy densities

Summary  We propose a partially adaptive estimator based on information theoretic maximum entropy estimates of the error distribution. The maximum entropy (maxent) densities have simple yet flexible functional forms to nest most of the mathematical distributions. Unlike the non‐parametric fully adaptive estimators, our parametric estimators do not involve choosing a bandwidth or trimming, and only require estimating a small number of nuisance parameters, which is desirable when the sample size is small. Monte Carlo simulations suggest that the proposed estimators fare well with non‐normal error distributions. When the errors are normal, the efficiency loss due to redundant nuisance parameters is negligible as the proposed error densities nest the normal. The proposed partially adaptive estimator compares favourably with existing methods, especially when the sample size is small. We apply the estimator to a stochastic frontier model, whose error distribution is usually non‐normal.