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An event encountered for the first time can become a common phenomenon in a population through transmission over time. This study focuses on nonparametric partially sequential test statistics in order to early detect such events. For this purpose, firstly, the partially sequential test statistic given in Mukherjee [1] is considered. Then, with a modification of this statistic, a new nonparametric partially sequential test statistic that works at almost the desired α level of significance is revealed. Also, based on Monte-Carlo simulations, the proposed test statistic is shown to be more powerful than Mukherjee's statistic. Lastly, two illustrative numerical examples are also given. [ABSTRACT FROM AUTHOR]

We develop Shiryaev–Roberts schemes based on signed sequential ranks to detect a persistent change in location of a continuous symmetric distribution with known median. The in‐control properties of these schemes are distribution‐free, hence they do not require a parametric specification of an underlying density function or the existence of any moments. Tables of control limits are provided. The out‐of‐control average run length properties of the schemes are gauged via theory‐based calculations and Monte Carlo simulation. Comparisons are made with two existing distribution‐free schemes. We conclude that the newly proposed scheme has much to recommend its use in practice. Implementation of the methodology is illustrated in an application to a data set from an industrial environment. [ABSTRACT FROM AUTHOR]

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. A novel approach permits the inclusion of a priori information in the form of quantiles. It is developed as a strategy to increase the sensitivity of the scoring statistic. The result is a powerful convenient method to analyze non normal data sequences. Also, four variations of sequential normal scores are presented using examples from the literature. Researchers and practitioners might find this approach useful to develop nonparametric procedures to address new problems extending the use of parametric procedures when distributional assumptions are not met. These methods are especially useful with large data streams where efficient computational methods are required. [ABSTRACT FROM PUBLISHER]

Sequential ranks are defined as ranks of such observations, which have been observed so far in a sequential design. This article studies hypotheses tests based on sequential ranks for different situations. The locally most powerful sequential rank test is derived for the hypothesis of randomness against a general alternative, including the two-sample difference in location or regression in location as special cases for the alternative hypothesis. Further, the locally most powerful sequential rank tests are derived for the one-sample problem and for independence of two samples in an analogous spirit as the classical results of Hájek and Šidák (1967) for (classical) ranks. The locally most powerful tests are derived for a fixed sample size and the results bring arguments in favor of existing tests. In addition, we propose a sequential testing procedure based on these statistics of the locally most powerful tests. Principles of such sequential testing are explained on the two-sample Wilcoxon test based on sequential ranks. [ABSTRACT FROM PUBLISHER]