论文标题
关于多项式分布中拟合优点测试的中间渐近效率
On the intermediate asymptotic efficiency of goodness-of-fit tests in multinomial distributions
论文作者
论文摘要
我们考虑通过基于一类对称统计的测试来考虑对多项式分布的均匀性测试，定义为细胞频率的某些功能之和。我们正在处理一个渐近状态，其中细胞数量随样本量而生长。大多数注意力集中在功率差异统计的类别上。本文的目的是研究两种测试的中间渐近相对效率，其中该测试的功能在渐近非分类中，而替代方案的序列融合到了假设，但不太快。卡方检验的中间渐近相对效率详细考虑了任意对称测试。
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime, where the number of cells grows with the sample size. Most attention is focused on the class of power divergence statistics. The aim of this article is to study the intermediate asymptotic relative efficiency of two tests, where the powers of the tests are asymptotically non-degenerate and the sequences of alternatives converge to the hypothesis, but not too fast. The intermediate asymptotic relative efficiency of the chi-square test wrt an arbitrary symmetric test is considered in details.
