The sequential normal scores transformation

摘要

The sequential analysis of series often requires nonparametric procedures, where the most powerful ones frequently use rank transformations. Reranking the data sequence after each new observation can become too intensive computationally. This led to the idea of sequential ranks, where only the most recent observation is ranked. However, difficulties finding, or approximating, the null distribution of the statistics may have contributed to the lack of popularity of these methods. In this article, we propose transforming the sequential ranks into sequential normal scores that are independent and asymptotically standard normal random variables. Thus, original methods based on the normality assumption may be used.