Information-Theoretic Distribution Test with Application to Normality

We derive general distribution tests based on the method of Maximum Entropy density. The proposed tests are derived from maximizing the differential entropy subject to moment constraints. By exploiting the equivalence between the Maximum Entropy and Maximum Likelihood estimates of the general exponential family, we can use the conventional Likelihood Ratio, Wald and Lagrange Multiplier testing principles in the maximum entropy framework. In particular, we use the Lagrange Multiplier method to derive tests for normality and their asymptotic properties. Monte Carlo evidence suggests that the proposed tests have desirable small sample properties and often outperform commonly used tests such as the Jarque-Bera test and the KolmogorovSmirnov-Lillie test for normality. We show that the proposed tests can be extended to tests based on regression residuals and non-iid data in a straightforward manner. We apply the proposed tests to the residuals from a stochastic production frontier model and reject the normality hypothesis. ∗Department of Economics, University of Guelph. Email: [email protected]. †Corresponding author. Department of Agricultural Economics, Texas A&M University and Department of Economics, University of Guelph. Email: [email protected]. We want to thank seminar participants at Penn State University, the 2004 European Meeting of the Econometric Society and the 2004 Canadian Econometrics Study Group for comments. We also thank the associate editor and two referees for comments and suggestions that helped us improve this paper. Financial support from SSHRC of Canada is gratefully acknowledged. JEL code: C1, C12, C16;