Goodness of Fit Tests and Entropy
TEXAS A AND M UNIV COLLEGE STATION DEPT OF STATISTICS
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This paper discusses the unifying role of entropy statistics and concepts in developing goodness of fit tests for a parametric model Fx for a continuous distribution function Fx, given an random sample from the distribution F. Statistics discussed are those by Moran extended by Cheng and Stephens, Vasicek and Dudewicz van der Meulen based on gap estimators of quantile density function, Parzen autoregressive estimators of quantile density functions, and shapiro and Wilk. They are given unified formulations as entropy difference statistics. Their 95 significance levels for sample sizes 20 and 50 are compared and shown to increase as amount of smoothing decreases. Keywords Goodness of fit Entropy Morans statistic Information divergence Gap estimators Autoregressive estimation Shapiro Wilk statistic.
- Statistics and Probability