Mathematical Sciences: Limit Distributions of GL-Related Statistics and Testing Independence of Circular Data

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The limit distributions of GL-statistics with kernels which are degenerate, of infinite order, or with estimated parameters are proposed. The underlying invariance principle of ``averaging Kendall's tau on its marginals'' is also proposed. Furthermore, an approach to derive new test statistics from some distances for independence of circular data is proposed. Finally, a unifying theme for many circular rank statistics will be investigated.