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.     

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.     

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.     

Assessing the fit of finite mixture distributions

Mixture distributions have become a very flexible and common class of distributions, used in many different applications, but hardly any literature can be found on tests for assessing their goodness of fit. We propose two types of smooth tests of goodness of fit for mixture distributions. The first test is a genuine smooth test, and the second test makes explicit use of the mixture structure. In a simulation study the tests are compared to some traditional goodness of fit tests that, however, are not customised for mixture distributions. The first smooth test has overall good power and generally outperforms the other tests. The second smooth test is particularly suitable for assessing the fit of each component distribution separately. The tests are applicable to both continuous and discrete distributions and they are illustrated on three medical data sets.     

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.     

Parametric bootstrap and approximate tests for two Poisson variates

The parametric bootstrap tests and the asymptotic or approximate tests for detecting difference of two Poisson means are compared. The test statistics used are the Wald statistics with and without log-transformation, the Cox F statistic and the likelihood ratio statistic. It is found that the type I error rate of an asymptotic/approximate test may deviate too much from the nominal significance level α under some situations. It is recommended that we should use the parametric bootstrap tests, under which the four test statistics are similarly powerful and their type I error rates are all close to α. We apply the tests to breast cancer data and injurious motor vehicle crash data.     

A discussion of the question: for what use are tests of hypotheses and tests of significance

The author believes that tests provide a poor model of most real problems, usually so poor that their objectivity is tangential and often too poor to be useful.     

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.     

Divergence statistics: sampling properties and multinomial goodness of fit and divergence tests

φ-divergence .statistics are obtained by either replacing both distributions involved in the argument of the φ -divergence measure by their sample estimates or replacing one distribution and considering the other as given. The sampling properties of estimated divergence-type measures are investigated. Approximate means and variances are derived and asymptotic distributions are obtained. Tests of goodness of fit of observed frequencies to expected ones and tests of equality of divergences based on two or more multinomial samples are constructed.     

A Diagnostic Test for Normality Within the Power Exponential Family

This article develops the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions. The small sample power properties of the test are compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions. In addition, the finite sample power properties for nonnormal alternatives within the power exponential family are summarized by estimating response surfaces. The results suggest that the proposed text is computationally convenient and possesses relatively attractive power properties even against alternatives outside the power exponential family.     

The measurement of capital utilisation rates

A strategy using spline function interpolation is developed f o r estimating capital utilisation rates . Cobb-Douglas, CES and translog functional forms are used in estimation. Tests for functional forms are conducted leading t o t h e s e l e c t i o n of the Cobb-Douglas form. Quarterly series of estimated utilisation rates and excess capacity measures are presented.     

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。     

The problem of outlier tests in sample surveys

Outliers can occur as readily in samples from the finite populations (e.g. in sample surveys) as in samples from infinite populations. However, in the vast literature on outliers there is almost no mention of outlier tests for data from sample surveys. We examine the behaviour of some standard outlier test statistics for infinite populations when these are applied to finite populations, examining their properties by extensive simulation studies. Some anomalous results are obtained Nsuggesting a fundamental difficulty in testing outliers for the finite population case.     

Constructing narrower confidence intervals by inverting adaptive tests

We begin by describing how to find the limits of confidence intervals by using a few permutation tests of significance. Next, we demonstrate how the adaptive permutation test, which maintains its level of significance, produces confidence intervals that maintain their coverage probabilities. By inverting adaptive tests, adaptive confidence intervals can be found for any single parameter in a multiple regression model. These adaptive confidence intervals are often narrower than the traditional confidence intervals when the error distributions are long‐tailed or skewed. We show how much reduction in width can be achieved for the slopes in several multiple regression models and for the interaction effect in a two‐way design. An R function that can compute these adaptive confidence intervals is described and instructions are provided for its use with real data.     

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.     

Permuiation tesis for k-sample binomial data with comparisons of exact and approximate P-levels

Exact ksample permutation tests for binary data for three commonly encountered hypotheses tests are presented,, The tests are derived both under the population and randomization models . The generating function for the number of cases in the null distribution is obtained, The asymptotic distributions of the test statistics are derived . Actual significance levels are computed for the asymptotic test versions , Random sampling of the null distribution is suggested as a superior alternative to the asymptotics and an efficient computer technique for implementing the random sampling is described., finally, some numerical examples are presented and sample size guidelines given for computer implementation of the exact tests.     

Nonparametric tests for multivariate multi-sample locations based on data depth

Several nonparametric tests for multivariate multi-sample location problem are proposed in this paper. These tests are based on the notion of data depth, which is used to measure the centrality/outlyingness of a given point with respect to a given distribution or a data cloud. Proposed tests are completely nonparametric and implemented through the idea of permutation tests. Performance of the proposed tests is compared with existing parametric test and nonparametric test based on data depth. An extensive simulation study reveals that proposed tests are superior to the existing tests based on data depth with regard to power. Illustrations with real data are provided.     

Union-Intersection testing for outliers in multivariate normal data

The union-intersection approach to multivariate test construction is used to develop an alternative to Wilks' likelihood ratio test statistic for testing for two or more outliers in multivariate normal data. It is shown that critical values of both statistics are poorly approximated by Bonferroni bounds. Simulated critical values are presented for both statistics for significance levels 1% and 5%, for sample sizes 10(5)30, 40, 50, 75 and 100 for 2, 3, 4 and 5 dimensions. A power comparison of the two tests in the slippage of the mean model for generating outliers indicates that the union-intersection test is the more powerful when the slippages are close to collinear. Although Wilks' test remains the preference for general use, the union-intersection test could be valuable when such special structure in the data is suspected.     

Theoretical properties of tests for spatial clustering of count data

Testing for spatial clustering of count data is an important problem in spatial data analysis. Several procedures have been proposed to this end but despite their extensive use, studies of their fundamental theoretical properties are almost non‐existent. The authors suggest two conditions that any reasonable test for spatial clustering should satisfy. The latter are based on the notion that the null hypothesis should be rejected almost surely as the amount of spatial clustering tends to infinity. The authors show that the chisquared test and the Potthoff—Whittinghill V have both properties but that other classical tests do not.     

THE POWER AND SIZE OF NONPARAMETRIC TESTS FOR COMMON DISTRIBUTIONAL CHARACTERISTICS

This paper considers the power and size properties of some well known nonparametric linear rank tests for location and scale as well as the Kolmogorov-Smirnov omnibus test and proposed alternatives to it. Independence between some classes of linear rank tests is established facilitating their joint application. Monte Carlo study confirms the asymptotic power properties of the linear rank tests but raises concerns about their application in more general and practically relevant circumstances. It also indicates that the new omnibus tests constitute viable alternatives with superior properties to the Kolmogorov-Smirnov test in certain circumstances.