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Smoothed ranks are proposed for two or multi-sample location problems. The regular ranks in Wilcoxon's two sample test are replaced with smoothed ranks, and the shift parameter is estimated. Asymptotic properties of the smoothed rank estimator are shown and a hypothesis test is proposed. Moreover, the smoothed ranks are applied in the Kruskal–Wallis'sr-sample test and the power of the test is computed using regular and smoothed ranks. Examples and Monte Carlo simulations show that the smoothed ranks perform similarly to the traditional rank based estimators under contaminated normal or non-normal populations. [ABSTRACT FROM PUBLISHER]

Bonferroni correction procedures are commonly used for performing multiple hypothesis tests in linear data problems. Moreover, several improved Bonferroni type procedures have been proposed and shown that they attain a type-I error rate better than the classical Bonferroni approach, but all of the studies are considered for linear data problems. The circular data analysis is a developing field of statistics that lacks similar studies, and also lacks computer programs to implement Bonferroni procedures. The aim of this study is to perform a comparative study of improved Bonferroni procedures and also to provide a computer program in R that performs classical and improved Bonferroni procedures for circular data problems. [ABSTRACT FROM AUTHOR]

A new procedure of shift parameter estimation in the two-sample location problem is investigated and compared with existing estimators. The proposed procedure smooths the empirical distribution functions of each random sample and replaces empirical distribution functions in the two-sample Kolmogorov–Smirnov method. The smoothed Kolmogorov–Smirnov is minimized with respect to an arbitrary shift variable in order to find an estimate of the shift parameter. The proposed procedure can be considered the smoothed version of a very little known method of shift parameter estimation from Rao-Schuster-Littell (RSL) [Raoet al.,Estimation of shift and center of symmetry based on Kolmogorov–Smirnov statistics, Ann. Stat. 3(4) (1975), pp. 862–873]. Their estimator will be discussed and compared with the proposed estimator in this paper. An example and simulation studies have been performed to compare the proposed procedure with existing shift parameter estimators such as Hodges–Lehmann (H–L) and least squares in addition to RSL's estimator. The results show that the proposed estimator has lower mean-squared error as well as higher relative efficiency against RSL's estimator under normal or contaminated normal model assumptions. Moreover, the proposed estimator performs competitively against H–L and least-squares shift estimators. Smoother function and bandwidth selections are also discussed and several alternatives are proposed in the study. [ABSTRACT FROM AUTHOR]

Uniform scores test is a rank-based method that tests the homogeneity ofk-populations in circular data problems. The influence of ties on the uniform scores test has been emphasized by several authors in several articles and books. Moreover, it is suggested that the uniform scores test should be used with caution if ties are present in the data. This paper investigates the influence of ties on the uniform scores test by computing the power of the test using average, randomization, permutation, minimum, and maximum methods to break ties. Monte Carlo simulation is performed to compute the power of the test under several scenarios such as having 5% or 10% of ties and tie group structures in the data. The simulation study shows no significant difference among the methods under the existence of ties but the test loses its power when there are many ties or complicated group structures. Thus, randomization or average methods are equally powerful to break ties when applying uniform scores test. Also, it can be concluded thatk-sample uniform scores test can be used safely without sacrificing the power if there are only less than 5% of ties or at most two groups of a few ties. [ABSTRACT FROM AUTHOR]

This paper is about estimating shift parameter by using pairwise differences in the two-sample location problem, which assumes G(x)=F(x-Δ). The parameter Δ is called location shift parameter between populations of F(x) and G(x). Distribution and density functions of the pairwise differences can be found and used to construct a log likelihood function with respect to the shift parameter. An estimator of the shift parameter is found by Newton's one step algorithm from the log likelihood function. Asymptotic properties of the new estimator which is similar to a regular MLE estimator are shown under some regularity conditions. As an example, normal and Laplace Distribution model assumptions are investigated using the proposed approach. Moreover, a hypothesis testing procedure is developed and shown that pairwise difference approach is asymptotically equivalent to the Rao's score type likelihood test. [ABSTRACT FROM AUTHOR]