Search

SUMMARY Rao's score statistic is a standard tool for carrying out hypothesis tests. A unified approach is given which encompasses many common tests. When a suitable group structure is present, it is shown how the derivation of the test statistic can be simplified. An omnibus test of multivariate normality is derived as an example of group invariance. As another application of Rao score tests, a general method is given for constructing tests of independence.

Time series the asymptotic distribution of auto-correlation co-efficients directional data analysis on Watson's anova for directions compositional and shape data analysis the triangle in statistics new directions for shape analysis technical problems in inference tests of fit for logistic models spatial statistics how to charge for boundaries in a Pixel image statistics and genetics case studies on issues of public policy.

In 1918 von Mises discovered the circular probability distribution which now bears his name by studying the analogue on the circle of the Gaussian maximum likelihood characterization of the normal distribution on the line. Teicher [6] gave a specific condition on the density function for the Gaussian characterization to hold (see also Kagan, et al. [2], p, 411). It is shown in this paper that the same condition is sufficient for the von Mises characterization to be valid. The proof is based on Teicher’s approach, but the periodic nature of circular densities makes substantial modifications necessary. An extension to the hyperspherical case is also given.