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Data depth based nonparametric tests for multivariate multisample location problem are provided which extend the depth based nonparametric test for multivariate two-sample location problem by Shirke and Khorate (2018) [Shirke, D.T. and Khorate, S.D., 2018. Two-sample nonparametric test for testing equality of locations based on data depth. Journal of the Indian Society for Probability and Statistics, 19, pp. 9-23.] to the multi-sample setting. Proposed tests are based on the correlations among the depths of data points. Power comparison of proposed tests with the existing depth based nonparametric tests is provided using a simulation study based on a permutation test. Simulation study reveals that the proposed tests give comparable powers compared to the existing data depth based nonparametric tests. Proposed tests are illustrated with real life data sets. [ABSTRACT FROM AUTHOR]

A three-sample distribution-free test for detecting non-decreasing ordered alternatives is proposed to alleviate some of the problems in the existing tests, including the risk of frequent detection of a trend when it is not actually present. The test is based on the natural U-statistic estimation of the parameter γ = P (Y 1 ≤ Y 2 ≤ Y 3) where Y 1 , Y 2 , Y 3 are three independent continuous random variables. Actual levels of the test and power values in the case of equal variances for a variety of sample sizes and over a wide class of distributions under the null hypothesis and the alternative are obtained via simulation. The results indicate that the proposed test compares favorably with existing tests. In all simulations the nonparametric test provided relatively good power, accurate control over the size of the test, and better protection against false detection of a non-existing trend. [ABSTRACT FROM AUTHOR]

Testing of equality of scale parameters is one of the fundamental problems in Statistics and is useful in many fields such as agriculture, engineering, experimental methods and dose level testing. In this paper, we propose a new class of nonparametric tests, to test whether the scale parameters of all the populations are equal, or there is an umbrella ordering in the scale parameters. The proposed test is based on weighted linear combination of two-sample U-statistics. The optimal choice of weights is determined so that proposed tests have maximum efficiency. The comparison of proposed test with respect to existing tests is made in terms of Pitman asymptotic relative efficiency. A numerical example is provided for illustrative purpose. Power of the proposed test is also assessed using Monte Carlo simulation study. [ABSTRACT FROM AUTHOR]

When the power of different nonparametric tests is evaluated by simulation, the alternative hypothesis should be carefully designed to ensure validity of the results in the specific research field. In the article, we propose a probit-based progressive shift alternative that is more realistic than the simple shift alternative for skewed non-negative data that occur in many research areas. Our motivation comes from parasitology. The progressive shift alternative is used to compare the power of six location-scale tests and seven commonly used location tests for several skewed theoretical and empirical parasite distributions. It is shown that location-scale tests are more powerful than location tests. Programs for applying the methods studied in the article are freely available for download. [ABSTRACT FROM AUTHOR]

Many researches have used ranked set sampling (RSS) method instead of simple random sampling (SRS) to improve power of some nonparametric tests. In this study, the two-sample permutation test within multistage ranked set sampling (MSRSS) is proposed and investigated. The power of this test is compared with the SRS permutation test for some symmetric and asymmetric distributions through Monte Carlo simulations. It has been found that this test is more powerful than the SRS permutation test; its power increased by set size and/or number of cycles and/or number of stages. Symmetric distributions power increased better than asymmetric distributions power. [ABSTRACT FROM AUTHOR]

Serial independence is tested using two measures of the effects of noise reduction in chaotic data, proposed by Orzeszko (2005). The extensive Monte Carlo simulations on the size and power of the new permutation-based tests are performed. Four popular nonparametric tests for serial independence are employed as a benchmark. The conducted simulations show that the new tests may be effective tools for detecting different kinds of dependencies. Moreover, they can distinguish between nonlinearity in the mean and nonlinearity in the variance. [ABSTRACT FROM AUTHOR]

Two-sample comparisons belonging to basic class of statistical inference are extensively applied in practice. There is a rich statistical literature regarding different parametric methods to address these problems. In this context, most of the powerful techniques are assumed to be based on normally distributed populations. In practice, the alternative distributions of compared samples are commonly unknown. In this case, one can propose a combined test based on the following decision rules: (a) the likelihood-ratio test (LRT) for equality of two normal populations and (b) the Shapiro--Wilk (S-W) test for normality. The rules (a) and (b) can be merged by, e.g., using the Bonferroni correction technique to offer the correct comparison of the samples distribution. Alternatively, we propose the exact density-based empirical likelihood (DBEL) ratio test.We develop the tsc package as the first R package available to perform the two-sample comparisons using the exact test procedures: the LRT; the LRT combined with the S-W test; aswell as the newly developed DBEL ratio test. We demonstrate Monte Carlo (MC) results and a real data example to show an efficiency and excellent applicability of the developed procedure. [ABSTRACT FROM AUTHOR]

When the null hypothesis of Friedman’s test is rejected, there is a wide variety of multiple comparisons that can be used to determine which treatments differ from each other. We will discuss the contexts where different multiple comparisons should be applied, when the population follows some discrete distributions commonly used to model count data in biological and ecological fields. Our simulation study shows that sign test is very conservative. Fisher’s LSD and Tukey’s HSD tests computed with ranks are the most liberal. Theoretical considerations are illustrated with data of the Azores Buzzard (Buteo buteo rothschildi) population from Azores, Portugal. [ABSTRACT FROM PUBLISHER]

Nonparametric detection of a change in distribution is studied when observations are independent. We provide a general method for constructing distribution-free change point detection schemes that have approximately likelihood structures. This method utilizes principles of the maximum empirical likelihood (EL) approach to approximate powerful parametric likelihood ratios. The product of the approximation can be associated with entropy-based test statistics. Entropy-based tests have been well addressed in the literature in the context of powerful decision rules for goodness of fit. We extend the entropy-based technique, using the EL principles. CUSUM and Shiryayev-Roberts (SR) detection policies are shown to be powerful parametric likelihood tests for detecting a change in distribution. We apply the proposed method to obtain nonparametric forms of the CUSUM and SR procedures. A Monte Carlo study demonstrates that the proposed method provides very efficient tests when comparing with the classical procedures. An example based on a real data is provided to demonstrate implementation and effectiveness of the new tests. [ABSTRACT FROM AUTHOR]

The literature displays change point detection problems in the context of one of the key issues that belong to testing statistical hypotheses. The main focus in this article is to review recent retrospective change point policies and propose new relevant procedures. Commonly, applied quality control purposes have declared statements of the change point problems. Various biostatistical and engineering applications cause consideration of an extended form of the change point problem. In this article, we consider parametric and distribution free generalized change point detection policies, attending to different contexts of optimality and robustness of the procedures. We conducted a broad Monte Carlo study to compare various parametric and nonparametric tests, also investigating a sensitivity of the change point detection policies with respect to assumptions required for correct executions of the procedures. An example based on real biomarker measurements is provided to judge our conclusions. [ABSTRACT FROM AUTHOR]

In this article, we study the power of one-sample location tests under classical distributions and two supermodels which include the normal distribution as a special case. The distributions of the supermodels are chosen in such a way that they have equal distance to the normal as the logistic, uniform, double exponential, and the Cauchy, respectively. As a measure of distance we use the Lévy metric. The tests considered are two parametric tests, the t -test and a trimmed t -test, and two nonparametric tests, the sign test and the Wilcoxon signed-rank tests. It turns out that the power of the tests, first of all, does not depend on the Lévy distance but on the special chosen supermodel. [ABSTRACT FROM AUTHOR]

Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper presents a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations, such as testing equality of distributions against inequality or testing stochastic dominance of distributions in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distributions of the statistics (under F = G) can be calculated via recursion formulae. Two tables with critical values of the new statistics are included. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian bridge. The distribution functions and quantiles thereof are obtained by Monte Carlo simulation. Finally, the power functions of the two new tests based on area statistics are compared to the power functions of the tests based on the corresponding supremum statistics, i.e., statistics of the Kolmogorov-Smirnov type. [ABSTRACT FROM AUTHOR]