A necessary and suffcient condition for Pitman's asymptotic relative effciency (ARE) of the Kendall and Spearman correlation statistics for the independence test to be 1 is given, in terms of certain smoothness and nondegeneracy properties of the model. Corresponding easy to use and broadly applicable sufficient conditions are obtained, which are then illustrated on several known models of dependence. Effects of the presence or absence of the smoothness and/or nondegeneracy parts of the mentioned necessary and suffcient condition are demonstrated using certain specially constructed dependence models. A more general (than usual) version of Pitman's ARE is developed, with broader and easier to check conditions of applicability. This version of the ARE, which is then used in the rest of the paper, may also be of value elsewhere.

中文翻译：

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Kendall 和 Spearman 相关统计的渐近相对效率

根据模型的某些平滑性和非退化性质，给出了独立性检验的Kendall和Spearman相关统计量的Pitman渐近相对效率（ARE）为1的充要条件。获得了相应的易于使用和广泛适用的充分条件，然后在几个已知的依赖模型上进行了说明。使用某些特殊构建的依赖模型证明了上述必要和充分条件的平滑和/或非退化部分的存在或不存在的影响。开发了一个更通用（比平常）的 Pitman ARE 版本，具有更广泛和更容易检查适用条件的情况。这个版本的 ARE，然后在本文的其余部分中使用，也可能在其他地方有价值。