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1.
《统计学通讯:理论与方法》2012,41(16-17):3094-3109
In this article, multivariate extensions of the combination-based test statistics for the comparison of several treatments in the multivariate Randomized Complete Block designs are introduced in case of categorical response variables. Several tests for the multivariate Randomized Complete Block designs, including MANOVA procedure, are compared with the method proposed via a Monte Carlo simulation study. The method has also been applied to a real case study in the field of sensorial testing studies. Results suggest that in each experimental situation where normality of the supposed underlying continuous model is hard to justify and especially when errors have heavy-tailed distributions, the proposed nonparametric procedure can be considered as a valid solution.  相似文献   

2.
In large-scale genomics experiments involving thousands of statistical tests, such as association scans and microarray expression experiments, a key question is: Which of the L tests represent true associations (TAs)? The traditional way to control false findings is via individual adjustments. In the presence of multiple TAs, p-value combination methods offer certain advantages. Both Fisher's and Lancaster's combination methods use an inverse gamma transformation. We identify the relation of the shape parameter of that distribution to the implicit threshold value; p-values below that threshold are favored by the inverse gamma method (GM). We explore this feature to improve power over Fisher's method when L is large and the number of TAs is moderate. However, the improvement in power provided by combination methods is at the expense of a weaker claim made upon rejection of the null hypothesis - that there are some TAs among the L tests. Thus, GM remains a global test. To allow a stronger claim about a subset of p-values that is smaller than L, we investigate two methods with an explicit truncation: the rank truncated product method (RTP) that combines the first K-ordered p-values, and the truncated product method (TPM) that combines p-values that are smaller than a specified threshold. We conclude that TPM allows claims to be made about subsets of p-values, while the claim of the RTP is, like GM, more appropriately about all L tests. GM gives somewhat higher power than TPM, RTP, Fisher, and Simes methods across a range of simulations.  相似文献   

3.
Split-plot design may be refer to a common experimental setting where a particular type of restricted randomization has occurred during a planned experiment. The aim of this article is to suggest a new method to perform inference on split-plot experiments by combination-based permutation tests. This novel nonparametric approach has been studied and validated using a Monte Carlo simulation study where we compared it with the parametric and nonparametric procedures proposed in the literature. Results suggest that in each experimental situation where normality is hard to justify and especially when errors have heavy-tailed distribution, the proposed nonparametric procedure can be considered as a valid solution.  相似文献   

4.
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.  相似文献   

5.
In several sciences, especially when dealing with performance evaluation, complex testing problems may arise due in particular to the presence of multidimensional categorical data. In such cases the application of nonparametric methods can represent a reasonable approach. In this paper, we consider the problem of testing whether a “treatment” is stochastically larger than a “control” when univariate and multivariate ordinal categorical data are present. We propose a solution based on the nonparametric combination of dependent permutation tests (Pesarin in Multivariate permutation test with application to biostatistics. Wiley, Chichester, 2001), on variable transformation, and on tests on moments. The solution requires the transformation of categorical response variables into numeric variables and the breaking up of the original problem’s hypotheses into partial sub-hypotheses regarding the moments of the transformed variables. This type of problem is considered to be almost impossible to analyze within likelihood ratio tests, especially in the multivariate case (Wang in J Am Stat Assoc 91:1676–1683, 1996). A comparative simulation study is also presented along with an application example.  相似文献   

6.
Two analysis of means type randomization tests for testing the equality of I variances for unbalanced designs are presented. Randomization techniques for testing statistical hypotheses can be used when parametric tests are inappropriate. Suppose that I independent samples have been collected. Randomization tests are based on shuffles or rearrangements of the (combined) sample. Putting each of the I samples ‘in a bowl’ forms the combined sample. Drawing samples ‘from the bowl’ forms a shuffle. Shuffles can be made with replacement (bootstrap shuffling) or without replacement (permutation shuffling). The tests that are presented offer two advantages. They are robust to non-normality and they allow the user to graphically present the results via a decision chart similar to a Shewhart control chart. A Monte Carlo study is used to verify that the permutation version of the tests exhibit excellent power when compared to other robust tests. The Monte Carlo study also identifies circumstances under which the popular Levene's test fails.  相似文献   

7.
Generalized discriminant analysis based on distances   总被引:14,自引:1,他引:13  
This paper describes a method of generalized discriminant analysis based on a dissimilarity matrix to test for differences in a priori groups of multivariate observations. Use of classical multidimensional scaling produces a low‐dimensional representation of the data for which Euclidean distances approximate the original dissimilarities. The resulting scores are then analysed using discriminant analysis, giving tests based on the canonical correlations. The asymptotic distributions of these statistics under permutations of the observations are shown to be invariant to changes in the distributions of the original variables, unlike the distributions of the multi‐response permutation test statistics which have been considered by other workers for testing differences among groups. This canonical method is applied to multivariate fish assemblage data, with Monte Carlo simulations to make power comparisons and to compare theoretical results and empirical distributions. The paper proposes classification based on distances. Error rates are estimated using cross‐validation.  相似文献   

8.
In this article, three methods of combining dependent univariate tests are studied. The Bahadur approximate efficiencies are derived under the asymptotic normal assumption. These procedures are applied to the multivariate location problem and compared with two Hotelling-type tests. A Monte Carlo study indicates that in certain cases the powers of the combination methods are much better than Hotelling's T 2 and other multivariate nonparametric tests.  相似文献   

9.
Peto and Peto (1972) have studied rank invariant tests to compare two survival curves for right censored data. We apply their tests, including the logrank test and the generalized Wilcoxon test, to left truncated and interval censored data. The significance levels of the tests are approximated by Monte Carlo permutation tests. Simulation studies are conducted to show their size and power under different distributional differences. In particular, the logrank test works well under the Cox proportional hazards alternatives, as for the usual right censored data. The methods are illustrated by the analysis of the Massachusetts Health Care Panel Study dataset.  相似文献   

10.
We introduce classical approaches for testing hypotheses on the meiosis I non disjunction fraction in trisomies, such as the likelihood-ratio, bootstrap, and Monte Carlo procedures. To calculate the p-values for the bootstrap and Monte Carlo procedures, different transformations in the data are considered. Bootstrap confidence intervals are also used as a tool to perform hypotheses tests. A Monte Carlo study is carried out to compare the proposed test procedures with two Bayesian ones: Jeffreys and Pereira-Stern tests. The results show that the likelihood-ratio and the Bayesian tests present the best performance. Down syndrome data are analyzed to illustrate the procedures.  相似文献   

11.
This article deals with the problem of classifying and ranking several multivariate populations of interests using the permutation and combination approach providing also an inferential validity of the procedure. The need to define an appropriate classification of populations, i.e., products, services, teaching courses, degree programs, and so on, is very common within many areas of applied research. Many times the populations of interest are multivariate in nature meaning that many aspects of that populations can be simultaneously observed on the same unit/subject. From a statistical point of view, when the response variable of interest is multivariate in nature, the problem may become quite difficult to cope with especially in case of ordered categorical responses, due to the large dimensionality of the parametric space. Nonparametric inference based on the NPC methodology however, allows us to overcome these limitations, without the need of referring to assume any specified random distribution.  相似文献   

12.
In this article the problem of comparing distributional heterogeneities for categorical variables is addressed. Specifically, the one-sided testing problem for heterogeneity comparisons is considered. For such a problem a bootstrap method is proposed and compared with a permutation method already present in literature. The power behavior of the two methods is compared through a Monte Carlo simulation study. The results of two real applications are shown.  相似文献   

13.
In this article, we propose a new multiple test procedure for assessing multivariate normality, which combines BHEP (Baringhaus–Henze–Epps–Pulley) tests by considering extreme and nonextreme choices of the tuning parameter in the definition of the BHEP test statistic. Monte Carlo power comparisons indicate that the new test presents a reasonable power against a wide range of alternative distributions, showing itself to be competitive against the most recommended procedures for testing a multivariate hypothesis of normality. We further illustrate the use of the new test for the Fisher Iris dataset.  相似文献   

14.
《统计学通讯:理论与方法》2012,41(16-17):2991-3001
A test for the fixed effect in mixed-models is proposed. It is based on permutation strategy and is exact. The testing approach presented is very general and the class of models covered is very broad.

Multivariate responses with different type of variables (e.g., continuous, categorical, and ranks) are usually tested with separated models and the overall test are usually reached through Bonferroni-like combinations, i.e., without taking into account the joint distribution of the test statistics. On the contrary, in this approach the joint distribution is immediately obtained and the dependence among tests is taken into account in the overall test. The methods are implemented in the R package flip, freely available on CRAN.  相似文献   

15.
A linear combination test for combining several tests of the correlation coefficient in the bivariate normal distribution is proposed. The linear combination test is compared with the well-known Fisher method of combining tests. It is shown by a Monte Carlo study that the linear combination test has a larger power.  相似文献   

16.
17.
Multiple hypothesis testing is widely used to evaluate scientific studies involving statistical tests. However, for many of these tests, p values are not available and are thus often approximated using Monte Carlo tests such as permutation tests or bootstrap tests. This article presents a simple algorithm based on Thompson Sampling to test multiple hypotheses. It works with arbitrary multiple testing procedures, in particular with step-up and step-down procedures. Its main feature is to sequentially allocate Monte Carlo effort, generating more Monte Carlo samples for tests whose decisions are so far less certain. A simulation study demonstrates that for a low computational effort, the new approach yields a higher power and a higher degree of reproducibility of its results than previously suggested methods.  相似文献   

18.
ABSTRACT

Asymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil’s index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power.  相似文献   

19.
Multivariate combination-based permutation tests have been widely used in many complex problems. In this paper we focus on the equipower property, derived directly from the finite-sample consistency property, and we analyze the impact of the dependency structure on the combined tests. At first, we consider the finite-sample consistency property which assumes that sample sizes are fixed (and possibly small) and considers on each subject a large number of informative variables. Moreover, since permutation test statistics do not require to be standardized, we need not assume that data are homoscedastic in the alternative. The equipower property is then derived from these two notions: consider the unconditional permutation power of a test statistic T for fixed sample sizes, with V ? 2 independent and identically distributed variables and fixed effect δ, calculated in two ways: (i) by considering two V-dimensional samples sized m1 and m2, respectively; (ii) by considering two unidimensional samples sized n1 = Vm1 and n2 = Vm2, respectively. Since the unconditional power essentially depends on the non centrality induced by T, and two ways are provided with exactly the same likelihood and the same non centrality, we show that they are provided with the same power function, at least approximately. As regards both investigating the equipower property and the power behavior in presence of correlation we performed an extensive simulation study.  相似文献   

20.
Many nonparametric tests in one sample problem, matched pairs, and competingrisks under censoring have the same underlying permutation distribution. This article proposes a saddlepoint approximation to the exact p-values of these tests instead of the asymptotic approximations. The performance of the saddlepoint approximation is assessed by using simulation studies that show the superiority of the saddlepoint methods over the asymptotic approximations in several settings. The use of the saddlepoint to approximate the p-values of class of two sample tests under complete randomized design is also discussed.  相似文献   

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