标题： 计算欧几里得距离拟合优度检验的渐近功效 显示英文标题

标题： Computing the asymptotic power of a Euclidean-distance test for goodness-of-fit

摘要： 一种自然（但非常规）的拟合优度检验方法通过欧几里得距离（或等价地，其平方）来衡量模型与经验分布之间的差异。 本文刻画了在这种检验对一类备择分布的统计功效，当观测数量趋于无穷大时，所有备择分布均以相同方向偏离模型。 具体而言，文章提供了一种高效的数值方法，在观测数量趋于无穷大的极限下，计算模型与经验分布之间欧几里得距离平方的累积分布函数（CDF）。 文章通过绘制几个例子的渐近功效（作为显著性水平的函数）来展示该方案。 显示英文摘要

摘要： A natural (yet unconventional) test for goodness-of-fit measures the discrepancy between the model and empirical distributions via their Euclidean distance (or, equivalently, via its square). The present paper characterizes the statistical power of such a test against a family of alternative distributions, in the limit that the number of observations is large, with every alternative departing from the model in the same direction. Specifically, the paper provides an efficient numerical method for evaluating the cumulative distribution function (cdf) of the square of the Euclidean distance between the model and empirical distributions under the alternatives, in the limit that the number of observations is large. The paper illustrates the scheme by plotting the asymptotic power (as a function of the significance level) for several examples.