An alternative formulation of Neyman's smooth goodness of fit tests under composite alternatives
We propose a natural extension of Neyman's smooth goodness of fit tests under composite hypotheses. The components of our smooth tests are immediate analogues of the corresponding components in the completely specified null case. We show that, when testing for univariate normality, one of our smooth tests is similar to \textit{R. D'Agostino} and \textit{E. S. Pearson}'s statistic [Biometrika 60, 613-622 (1973; Zbl 0271.62025)]; when testing for multivariate normality, out smooth test for skewness is identical to \textit{K. V. Mardia}'s measure of multivariate skewness [ibid. 57, 519-530 (1970; Zbl 0214.463)] and, when testing for exponentiality, our simplest smooth test is equivalent to \textit{M. Greenwood}'s statistic [The statistical study of infectious disease. J. R. Stat. Soc. (N.S.) 109, 85-110 (1946)].
scientific article; zbMATH DE number 3992663