Information-Theoretic Distribution Test with Application to Normality
基于最大熵密度方法推导出一般分布检验，利用似然比、Wald和拉格朗日乘子检验原理，特别用拉格朗日乘子法构造正态性检验，蒙特卡洛证据表明其与常用检验相当或更优，并可扩展到回归残差和非独立同分布数据。
We derive general distribution tests based on the method of maximum entropy (ME) density. The proposed tests are derived from maximizing the differential entropy subject to given moment constraints. By exploiting the equivalence between the ME and maximum likelihood (ML) estimates for the general exponential family, we can use the conventional likelihood ratio (LR), Wald, and Lagrange multiplier (LM) testing principles in the maximum entropy framework. In particular, we use the LM approach to derive tests for normality. Monte Carlo evidence suggests that the proposed tests are compatible with and sometimes outperform some commonly used normality tests. We show that the proposed tests can be extended to tests based on regression residuals and non-i.i.d. data in a straightforward manner. An empirical example on production function estimation is presented.