Permutation Testing for Monotone “Trend”
研究了时间序列中单调趋势的检验问题，指出Mann-Kendall检验在大样本下也无法控制第一类错误，而通过学生化构造的置换检验能渐近控制错误率，并保持独立同分布数据下的精确性，还引入了局部Mann-Kendall统计量用于检验局部趋势。
ABSTRACT In this article, we consider the fundamental problem of testing for monotone trend in a time series. While the term “trend” is commonly used and has an intuitive meaning, it is first crucial to specify its exact meaning in a hypothesis testing context. A commonly used well‐known test is the Mann‐Kendall test, which we show does not offer Type 1 error control even in large samples. On the other hand, by an appropriate studentization of the Mann‐Kendall statistic, we construct permutation tests that offer asymptotic error control quite generally, but retain the exactness property of permutation tests for i.i.d. observations. We also introduce “local” Mann‐Kendall statistics as a means of testing for local rather than global trend in a time series. Similar properties of permutation tests are obtained for these tests as well.