Permutation tests for homogeneity based on some characterizations

In this work, non parametric tests are proposed for testing the homogeneity of two or more populations. The tests are based on recently obtained characterizations. The test procedure is based on the permutation bootstrap technique. For the two-sample case the new tests are compared with permutation tests based on the empirical characteristic function and some other tests. The comparison is fulfilled via a Monte Carlo simulation.     

Test for normality based on two new estimators of entropy

In this article, two new consistent estimators are introduced of Shannon's entropy that compares root of mean-square error with other estimators. Then we define new tests for normality based on these new estimators. Finally, by simulation, the powers of the proposed tests are compared under different alternatives with other entropy tests for normality.     

Exact tests based on the Baumgartner-Weiß-Schindler statistic—A survey

It is the purpose of this paper to review recently-proposed exact tests based on the Baumgartner-Weiß-Schindler statistic and its modification. Except for the generalized Behrens-Fisher problem, these tests are broadly applicable, and they can be used to compare two groups irrespective of whether or not ties occur. In addition, a nonparametric trend test and a trend test for binomial proportions are possible. These exact tests are preferable to commonly-applied tests, such as the Wilcoxon rank sum test, in terms of both type I error rate and power.     

Methods for testing subblock patterns

A number of statistical tests have been recommended over the last twenty years for assessing the randomness of long binary strings used in cryptographic algorithms. Several of these tests include methods of examining subblock patterns. These tests are the uniformity test, the universal test and the repetition test. The effectiveness of these tests are compared based on the subblock length, the limitations on data requirements, and on their power in detecting deviations from randomness. Due to the complexity of the test statistics, the power functions are estimated by simulation methods. The results show that for small subblocks the uniformity test is more powerful than the universal test, and that there is some doubt about the parameters of the hypothesised distribution for the universal test statistic. For larger subblocks the results show that the repetition test is the most effective test, since it requires far less data than either of the other two tests and is an efficient test in detecting deviations from randomness in binary strings.     

Maximum Average-Power (MAP) Tests

The objective of this article is to propose and study frequentist tests that have maximum average power, averaging with respect to some specified weight function. First, some relationships between these tests, called maximum average-power (MAP) tests, and most powerful or uniformly most powerful tests are presented. Second, the existence of a maximum average-power test for any hypothesis testing problem is shown. Third, an MAP test for any hypothesis testing problem with a simple null hypothesis is constructed, including some interesting classical examples. Fourth, an MAP test for a hypothesis testing problem with a composite null hypothesis is discussed. From any one-parameter exponential family, a commonly used UMPU test is shown to be also an MAP test with respect to a rich class of weight functions. Finally, some remarks are given to conclude the article.     

A monte carlo study of the wald,lm, and lr tests in a heteroscedastic linear model

In this paper, we examine by Monte Carlo experiments the small sample properties of the W (Wald), LM (Lagrange Multiplier) and LR (Likelihood Ratio) tests for equality between sets of coefficients in two linear regressions under heteroscedasticity. The small sample properties of the size-corrected W, LM and LR tests proposed by Rothenberg (1984) are also examined and it is shown that the performances of the size-corrected W and LM tests are very good. Further, we examine the two-stage test which consists of a test for homoscedasticity followed by the Chow (1960) test if homoscedasticity is indicated or one of the W, LM or LR tests if heteroscedasticity should be assumed. It is shown that the pretest does not reduce much the bias in the size when the sizecorrected citical values are used in the W, LM and LR tests.     

Small sample power of multivariate nonparametric tests for monotone trend

Bhattacharyya and Kioiz (1966) propose two multivariate nonparametric tests for monotone trend, one involving coordinate-wise Mann statistics and the other, coordinate-wise Spearman statistics. Dietz and Killeen (1981) propose a different test statistic based on coordinate-wise Mann statistics. The Pitman asymptotic relative efficiency of all three tests with respect to a normal theory competitor equals the cube root of the efficiency of a multivariate signed rank test with respect to Hotelling's T2. In this article, the small sample power of the nonparametric tests, the normal theory test, and a Bonferroni approach involving coordinate-wise univariate Mann or Spearman tests is examined in a simulation study. The Mann statistic of Dietz and Killeen and the Spearman statistic of Bhattacharyya and Klotz are found to perform well under both null and alternative hypotheses     

RAO'S SCORE TESTS IN SURVIVAL ANALYSIS: EXAMPLES AND BARTLETT TYPE ADJUSTMENTS

Score method in hypothesis testing is one of Professor C. R. Rao's great contributions to statistics. It provides a simple and unified way to test some simple and composite hypotheses in many statistical problems. Some popular tests in statistical practice derived with the help of intuitions can be shown as score tests under some statistical models. The subject-years test and log-rank test in survival analysis are two of the examples. In this paper, we first introduce these two examples. After formulating these two tests as score tests, we then review some recent results on the Bartlett type adjustments for these tests.     

Simultaneous tests for homogeneity of two zero-inflated (beta) populations

ABSTRACT

Motivated by an example in marine science, we use Fisher’s method to combine independent likelihood ratio tests (LRTs) and asymptotic independent score tests to assess the equivalence of two zero-inflated Beta populations (mixture distributions with three parameters). For each test, test statistics for the three individual parameters are combined into a single statistic to address the overall difference between the two populations. We also develop non parametric and semiparametric permutation-based tests for simultaneously comparing two or three features of unknown populations. Simulations show that the likelihood-based tests perform well for large sample sizes and that the statistics based on combining LRT statistics outperforms the ones based on combining score test statistics. The permutation-based tests have overall better performance in terms of both power and type I error rate. Our methods are easy to implement and computationally efficient, and can be expanded to more than two populations and to other multiple parameter families. The permutation tests are entirely generic and can be useful in various applications dealing with zero (or other) inflation.     

Rotation test with pairwise distance measures of sample vectors in a GLM

One way to cope with high-dimensional data even in small samples is the use of pairwise distance measures—such as the Euclidean distance—between the sample vectors. This is usually done with permutation tests. Here we propose the application of exact parametric rotation tests which are no longer restricted by the finite number of possible permutations of a sample. The method is presented in the framework of the general linear model.     

PERMUTATION TESTS AND OTHER TEST STATISTICS FOR ILL-BEHAVED DATA: EXPERIENCE OF THE NINDS t-PA STROKE TRIAL

Permutation tests are often used to analyze data since they may not require one to make assumptions regarding the form of the distribution to have a random and independent sample selection. We initially considered a permutation test to assess the treatment effect on computed tomography lesion volume in the National Institute of Neurological Disorders and Stroke (NINDS) t-PA Stroke Trial, which has highly skewed data. However, we encountered difficulties in summarizing the permutation test results on the lesion volume. In this paper, we discuss some aspects of permutation tests and illustrate our findings. This experience with the NINDS t-PA Stroke Trial data emphasizes that permutation tests are useful for clinical trials and can be used to validate assumptions of an observed test statistic. The permutation test places fewer restrictions on the underlying distribution but is not always distribution-free or an exact test, especially for ill-behaved data. Quasi-likelihood estimation using the generalized estimating equation (GEE) approach on transformed data seems to be a good choice for analyzing CT lesion data, based on both its corresponding permutation test and its clinical interpretation.     

Goodness-of-Fit Tests for the Gamma Distribution Based on the Empirical Laplace Transform

We propose a class of goodness-of-fit tests for the gamma distribution that utilizes the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution under the null hypothesis are investigated. As the decay of the weight function tends to infinity, the test statistics approach limit values related to the first non zero component of Neyman's smooth test for the gamma law. The new tests are compared with other omnibus tests for the gamma distribution.     

Linear signed rank tests for hultivariate location

Previously proposed linear signed rank tests for multivariate location are not invariant under linear transformations of the observations, The asymptotic relative efficiencies of the tests 2 with respect to Hotelling's T²test depend on the direction of shift and the covariance matrix of the alternative distributions. For distributions with highly correlated components, the efficiencies of some of these tests can be arbitrarily low; they approach zero for certain multivariate normal alternatives, This article proposes a transformation of the data to be performed prior to standard linear signed rank tests, The resulting procedures have attractive power and efficiency properties compared to the original tests, In particular, for elliptically symmetric contiguous alternafives, the efficiencies of the new tests equal those of corresponding univariate linear signed rank tests with respect to the t test.     

Permutation tests of scale using deviances

Robust tests for comparing scale parameters, based on deviances—absolute deviations from the median—are examined. Higgins (2004) proposed a permutation test for comparing two treatments based on the ratio of deviances, but the performance of this procedure has not been investigated. A simulation study examines the performance of Higgins’ test relative to other tests of scale utilizing deviances that have been shown in the literature to have good properties. An extension of Higgins’ procedure to three or more treatments is proposed, and a second simulation study compares its performance to other omnibus tests for comparing scale. While no procedure emerged as a preferred choice in every scenario, Higgins’ tests are found to perform well overall with respect to Type I error rate and power.     

Sequential LND sensitivity test for binary response data

Sensitivity tests are used to make inferences about a sensitivity, a characteristic property of some products that cannot be observed directly. For binary response sensitivity data (dead or alive, explode or unexplode), the Langlie and Neyer are two well-known sensitivity tests. The priorities of the Langlie and Neyer tests are investigated in this paper. It is shown that the Langlie test has an advantage in getting an overlap, while the Neyer test has better estimation precision. Aiming at improving both the speed of getting an overlap and the estimation precision, we propose a new sensitivity test which replaces the first part of the Neyer test with the Langlie test. Our simulation studies indicate that the proposed test outperforms the Langlie, Neyer and Dror and Steinberg tests from the viewpoints of estimation precision and probability of obtaining an overlap.     

A modified Mack–Wolfe test for the umbrella alternative problem

ABSTRACT

The Mack–Wolfe test is the most frequently used non parametric procedure for the umbrella alternative problem. In this paper, modifications of the Mack–Wolfe test are proposed for both known peak and unknown peak umbrellas. The exact mean and variance of the proposed tests in the null hypothesis are also derived. We compare these tests with some of the existing tests in terms of the type I error rate and power. In addition, a real data example is presented.     

On the Exact Size of Tests of Treatment Effects in Multi‐Arm Clinical Trials

When testing treatment effects in multi‐arm clinical trials, the Bonferroni method or the method of Simes 1986) is used to adjust for the multiple comparisons. When control of the family‐wise error rate is required, these methods are combined with the close testing principle of Marcus et al. (1976). Under weak assumptions, the resulting p‐values all give rise to valid tests provided that the basic test used for each treatment is valid. However, standard tests can be far from valid, especially when the endpoint is binary and when sample sizes are unbalanced, as is common in multi‐arm clinical trials. This paper looks at the relationship between size deviations of the component test and size deviations of the multiple comparison test. The conclusion is that multiple comparison tests are as imperfect as the basic tests at nominal size α/m where m is the number of treatments. This, admittedly not unexpected, conclusion implies that these methods should only be used when the component test is very accurate at small nominal sizes. For binary end‐points, this suggests use of the parametric bootstrap test. All these conclusions are supported by a detailed numerical study.     

Multivariate two‐sample permutation tests for trials with multiple time‐to‐event outcomes

Clinical trials involving multiple time‐to‐event outcomes are increasingly common. In this paper, permutation tests for testing for group differences in multivariate time‐to‐event data are proposed. Unlike other two‐sample tests for multivariate survival data, the proposed tests attain the nominal type I error rate. A simulation study shows that the proposed tests outperform their competitors when the degree of censored observations is sufficiently high. When the degree of censoring is low, it is seen that naive tests such as Hotelling's T² outperform tests tailored to survival data. Computational and practical aspects of the proposed tests are discussed, and their use is illustrated by analyses of three publicly available datasets. Implementations of the proposed tests are available in an accompanying R package.