The well-known Mann–Whitney–Wilcoxon (MWW) statistic is based on empirical distribution estimates. However, the data are often drawn from smooth populations. Therefore, smoothness characteristic not preserved. In addition, several authors have pointed out that an inadmissible estimate. Thus, in this work, we develop versions of MWW function This approach preserves characteristics and allows eff...

Gene set enrichment analysis (GSEA) is typically based on tests derived from the KolmogorovSmirnov, which is underpowered and a need for simpler methods has been identified.[2] The wgsea package contains functions for conducting GSEA using a Wilcoxon test to test for differences in the distribution of p values between SNPs within the gene set under test and a control set of SNPs. The mean of th...

where sgn(x) stands for the sign of x. We first present and prove two useful lemmas about the unpenalized weighted Wilcoxon estimator under possible local contamination. These results will be useful later to establish the asymptotic properties of the penalized Wilcoxon estimator. In the proof of the two lemmas, we frequently refer to the book of Hettmansperger and McKean (1998), abbreviated as ...

We extend the basic idea of Schwarz (1978) and develop a generalized Bayesian information criterion for regression model selection. The new criterion relaxes the usually strong distributional assumption associated with Schwarz’s BIC by adopting a Wilcoxon-type dispersion function and appropriately adjusting the penalty term. We establish that the Wilcoxon-type generalized BIC preserves the cons...

The rank statistics Sn(t) = 1 n ∑n i=1 ciRi(t) (t ∈ R), with Ri(t) being the rank of ei−txi, i = 1, . . . , n and e1, . . . , en being the random sample from the basic distribution with the cdf F , are considered as a random process with t in the role of parameter. Under some assumptions on ci, xi and on the underlying distribution, it is proved that the process {Sn( t √n)− Sn(0)− ESn(t), |t|2 ...

In this paper, we consider applying the Wilcoxon’s idea for the construction of the one-sample problem to the two-sample case. For this, we show that the location translation parameter becomes a median of the distribution of the difference of two independent random variables under the location translation model. Based on this fact, we construct generalized signed-rank statistics for the two sam...

SUMMARY New rank-based methods for analyzing data from multisite clinical trials are presented ·in the context of "mixed" linear models. In contrast to current rank methods, the new procedures test for a drug main effect in the presence of a random drug by site interaction (or drug by investigator interaction when there is only one investigator per site). Analogous procedures are also provided ...