Comparisons of smooth tests and Gini test for uniformity on the unit interval

In this paper we introduce the smooth tests and the Gini test for testing the null hypothesis of uniformity on the unit interval (0,1). The actual convergence rates of the two kinds of statistics approach to the asymptotic distributions are obtained by simulation. Power simulation shows that the effect order of smooth tests against various alternatives does not exist. While for a data set, the effect order can be determined by applying a sequence of the smooth tests to a particular alternative. The simulated power comparisons indicate that the smooth test of the effect order is more powerful than the Gini test based on spacings against a wide variety of alternatives. When the alternative distribution is very similar in shape to the null distribution, the first two components of the smooth test can be used to detect the errors in mean and variance, respectively.