On the Weak Consistency of Permutation Tests

Consistency of some nonparametric tests with real variables has been studied by several authors under the assumption that population variance is finite and/or in the presence of some violations of the data exchangeability between samples. Since main inferential conclusions of permutation tests concern the actual dataset, where sample sizes are held fixed, we consider the notion of consistency in the weak version (in probability). Here, we characterize weak consistency of permutation tests assuming population mean is finite and without assuming existence of population variance. Moreover, since permutation test statistics do not require to be standardized, we do not assume that data are homoscedastic in the alternative. Several application examples to mostly used test statistics are discussed. A simulation study and some hints for robust testing procedures are also presented.     

Weighted Logrank Permutation Tests for Randomly Right Censored Life Science Data

In biomedical research, weighted logrank tests are frequently applied to compare two samples of randomly right censored survival times. We address the question how to combine a number of weighted logrank statistics to achieve good power of the corresponding survival test for a whole linear space or cone of alternatives, which are given by hazard rates. This leads to a new class of semiparametric projection tests that are motivated by likelihood ratio tests for an asymptotic model. We show that these tests can be carried out as permutation tests and discuss their asymptotic properties. A simulation study together with the analysis of a classical data set illustrates the advantages.     

On Permutation Tests in Multiple Regression and Analysis of Covariance Problems

We introduce distribution-free permutation tests and corresponding estimates for studying the effect of a treatment variable x on a response y. The methods apply in the presence of a multivariate covariate z. They are based on the assumption that the treatment values are assigned randomly to the subjects.     

Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e., the maximization algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this article, we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.     

Exact Multivariate Permutation Tests for Fixed Effects in Mixed-Models

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.     

Conditional tests in a competing risks model

Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors. The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests. In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data). The resulting conditional tests are initially developed for the case of k = 2 and are then extended to k > 2 by performing a sequence of two sample tests and by combining several risks into one. A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power. A real life example is also discussed to show how to implement such conditional tests.     

Conditional inference under simultaneous stochastic ordering constraints

Testing for stochastic ordering is of considerable importance when increasing does of a treatment are being compared, but in applications involving multivariate responses has received much less attention. We propose a permutation test for testing against multivariate stochastic ordering. This test is distribution-free and no assumption is made about the dependence relations among variables. A comparative simulation study shows that the proposed solution exhibits a good overall performance when compared with existing tests that can be used for the same problem.     

Some Elementary Theory of Permutation Tests

In literature, permutation tests are mostly derived by means of heuristic arguments (Edgington and Onghena, 2007 Edgington, E.S., Onghena, P. (2007). Randomization Tests (4th ed.). Boca Raton: Chapman & Hall/CRC.[Crossref] , [Google Scholar]; Good, 2005 Good, P. (2005). Permutation, Parametric, and Bootstrap Tests of Hypotheses (3rd ed.). New York: Springer-Verlag. [Google Scholar]). In this paper, we derive them within the sufficiency and conditionality principles of inference. Most important of their properties are exposed without formal proofs that can be found in the book by Pesarin and Salmaso (2010).     

Conditional Studentized Survival Tests for Randomly Censored Models

It is shown that in the case of heterogenous censoring distributions Studentized survival tests can be carried out as conditional permutation tests given the order statistics and their censoring status. The result is based on a conditional central limit theorem for permutation statistics. It holds for linear test statistics as well as for sup-statistics. The procedure works under one of the following general circumstances for the two-sample problem: the unbalanced sample size case, highly censored data, certain non-convergent weight functions or under alternatives. For instance, the two-sample log rank test can be carried out asymptotically as a conditional test if the relative amount of uncensored observations vanishes asymptotically as long as the number of uncensored observations becomes infinite. Similar results hold whenever the sample sizes and are unbalanced in the sense that and hold.     

A Critical Review and a Comparative Study on Conditional Permutation Tests for Two-Way ANOVA

Two-way ANOVA methodology is surely one of the most important models in the framework of the experimental design theory, as suggested by the great number of proposed solutions given in literature. Among these, some solutions are nonparametric and particularly, thanks to the availability of modern powerful computing equipments, those based on conditional on observations permutation test have gained great interest. The aim of this work is to present and compare such proposals and to illustrate their possible advantages and disadvantages when applied to some real data-sets.     

A new random permutation test in ANOVA models

This paper developed an exact method of random permutations when testing both interaction and main effects in the two-way ANOVA model. The method of this paper can be regarded as a much improved model when compared with those of the previous studies such as Still and White (1981) and ter Braak (1992). We further conducted a simulation experiment in order to check the statistical performance of the proposed method. The proposed method works relatively well for small sample sizes compare with the existing methods. This work was supported by Korea Science and Engineering Foundation Grant (R14-2003-002-0100)     

Combination-Based Permutation Tests: Equipower Property and Power Behavior in Presence of Correlation

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.     

Covariate Order Tests for Covariate Effect

A new approach for constructing tests for association between a random right censored life time variable and a covariate is proposed. The basic idea is to first arrange the observations in increasing order of the covariate and then base the test on a certain point process defined by the observation times. Tests constructed by this approach are robust against outliers in the covariate values or misspecification of the covariate scale since they only use the ordering of the covariate. Of particular interest is a test based on the Anderson-Darling statistic. This test has good power properties both against monotonic and nonmonotonic dependencies between the covariate and the life time variable.     

Tests in a Case–control Design Including Relatives

Abstract.  We present a new approach to handle dependencies within the general framework of case–control designs, illustrating our approach by a particular application from the field of genetic epidemiology. The method is derived for parent–offspring trios, which will later be relaxed to more general family structures. For applications in genetic epidemiology we consider tests on equality of allele frequencies among cases and controls utilizing well-known risk measures to test for independence of phenotype and genotype at the observed locus. These test statistics are derived as functions of the entries in the associated contingency table containing the numbers of the alleles under consideration in the case and the control group. We find the joint asymptotic distribution of these entries, which enables us to derive critical values for any test constructed on this basis. A simulation study reveals the finite sample behaviour of our test statistics.     

On Non-Normal Invariance Principles for Multi-Response Permutation Procedures

A non-normal invariance principle is established for a restricted class of univariate multi-response permutation procedures whose distance measure is the square of Euclidean distance. For observations from a distribution with finite second moment, the test statistic is found asymptotically to have a centered chi-squared distribution. Spectral expansions are used to determine the asymptotic distribution for more general distance measures d, and it is shown that if d(x, y) = |x — y|^u, u? 2, the asymptotic distribution is not invariant (i.e. it is dependent on the distribution of the observations).     

On the Relationship between Directional and Omnibus Statistical Tests

Abstract.  A common statistical problem involves the testing of a K -dimensional parameter vector. In both parametric and semiparametric settings, two types of directional tests – linear combination and constrained tests – are frequently used instead of omnibus tests in hopes of achieving greater power for specific alternatives. In this paper, we consider the relationship between these directional tests, as well as their relationship to omnibus tests. Every constrained directional test is shown to be asymptotically equivalent to a specific linear combination test under a sequence of contiguous alternatives and vice versa. Even when the direction of the alternative is known, the constrained test in general will not be optimal unless the objective function used to derive it is efficient. For an arbitrary alternative, insight into the power characteristics of directional tests in comparison to omnibus tests can be gained by a chi-square partition of the omnibus test.     

On Augmented Franses Tests for Seasonal Unit Roots

This article extends the results reported in del Barrio Castro, Osborn and Taylor (2012 del Barrio Castro, T., Osborn, D.R., Taylor, A. M.R. (2012). On augmented HEGY tests for seasonal unit roots. Econometric Theor. 18:1121–1143.[Crossref], [Web of Science ®] , [Google Scholar]) to the approach followed by Franses (1991a Franses, P. H. (1991a). Model selection and seasonality in time series. Tibergen Institute Series, 18. [Google Scholar],b Franses, P.H. (1991b). Seasonality, non-stationarity and the forecasting of monthly time series. Int. J. Forecast. 7:199–208.[Crossref], [Web of Science ®] , [Google Scholar]) to test for seasonal unit roots, providing the asymptotic representation to the seasonal unit roots tests proposed by Franses for a general number of seasons S.     

Tests on the Equality of Two Multiple Correlation Coefficients

Asymptotic tests are suggested for testing the equality of two multiple correlation coefficients calculated from a single sample from a multivariate normal distribution. An F test is possible only when the two dependent variables coincide and one set of independent variables is a subset of the second set. Tests are compared by simulation for situations in which the F test is inapplicable. Special attention is paid to cases in which asymptotic normality of the test statistics does not hold.     

Normal Theory and Bootstrap Confidence Interval Estimation in Assessing Diagnostic Performance Gain When Combining Two Diagnostic Tests

Many diagnostic tests may be available to identify a particular disease. Diagnostic performance can be potentially improved by combining. “Either” and “both” positive strategies for combining tests have been discussed in the literature, where a gain in diagnostic performance is measured by a ratio of positive (negative) likelihood ratio of the combined test to that of an individual test. Normal theory and bootstrap confidence intervals are constructed for gains in likelihood ratios. The performance (coverage probability, width) of the two methods are compared via simulation. All confidence intervals perform satisfactorily for large samples, while bootstrap performs better in smaller samples in terms of coverage and width.     

空间动态面板模型的时间滞后效应检验

空间面板数据模型由于考虑了经济变量间的空间相关性,其优势日益凸显,已成为计量经济学的热点研究领域。将空间相关性与动态模式同时扩展到面板模型中的空间动态面板模型,不仅考虑了经济变量之间的空间相关性,还考虑了时间上的滞后性,是空间面板模型的发展,增强了模型的解释力。考虑一种带固定个体效应、因变量的时间滞后项、因变量与随机误差项均存在空间自相关性的空间动态面板回归模型,提出了在个体数n和时间数T都很大,且T相对地大于n的条件下空间动态面板模型中时间滞后效应存在性的LM和LR检验方法,其检验方法包括联合检验、一维及二维的边际和条件检验;推导出这些检验在零假设下的极限分布;其极限分布均服从卡方分布。通过模拟试验研究检验统计量的小样本性质,结果显示其具有优良的统计性质。