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Moran’s I is the most popular spatial test statistic, but its inability to incorporate heterogeneous populations has been long recognized. This article provides a limiting distribution of the Moran’s I coefficient which can be applied to heterogeneous populations. The method provides a unified framework of testing for spatial autocorrelation for both homogeneous and heterogeneous populations, thereby resolving a long standing issue for Moran’s I . For Poisson count data, a variance adjustment method is provided that solely depends on populations at risk. Simulation results are shown to be consistent with theoretical results. The application of Nebraska breast cancer data shows that the variance adjustment method is simple and effective in reducing type I error rates, which in turn will likely reduce potential misallocation of limited resources. [ABSTRACT FROM AUTHOR]

The use of { 2 } -inverses in Wald-type statistic for hypothesis testing in general factorial designs is investigated. In terms of size control and power, the proposed tests are comparable with existing tests for symmetric distributions of errors and better for skewed ones. [ABSTRACT FROM AUTHOR]

This short paper presents some personal considerations on the challenge that the outbreak of big data (which I prefer to call complex data) has posed to statistics as a discipline. I also unpretentiously indicate a possible (hopefully winning) strategy to tackle this challenge. [ABSTRACT FROM AUTHOR]

Abstract: A test for the serial independence of errors in panel data models is proposed. The test is based on the difference between the joint empirical characteristic function of residuals at different lags and the product of their marginal empirical characteristic functions. The test is nuisance-parameter-free and powerful against any type of pairwise dependence at all lags. A simple random permutation procedure is used to approximate the limit distribution of the test. A Monte Carlo experiment illustrates the finite sample performance of the test, and supports that the test statistic based on the estimated residuals has the same asymptotic distribution as the corresponding statistic based on the unobservable true errors. [Copyright &y& Elsevier]

Abstract: Permutation methods using median differences for simultaneous pairwise comparisons with a control are investigated. Simulation results suggest that the permutation methods are generally more powerful than the Dunnett procedure when data are from nonnormal distributions. A new procedure is shown to provide strong control of the familywise error rate, and have highest power for detecting the treatment that differs most from the control, for certain nonnormal distributions. Step-down permutation procedures, which have greater power to detect treatment differences with the control, are also proposed and examined. The procedures are illustrated using an example from the applied literature. [Copyright &y& Elsevier]

Abstract: A paired data set is common in microarray experiments, where the data are often incompletely observed for some pairs due to various technical reasons. In microarray paired data sets, it is of main interest to detect differentially expressed genes, which are usually identified by testing the equality of means of expressions within a pair. While much attention has been paid to testing mean equality with incomplete paired data in previous literature, the existing methods commonly assume the normality of data or rely on the large sample theory. In this paper, we propose a new test based on permutations, which is free from the normality assumption and large sample theory. We consider permutation statistics with linear mixtures of paired and unpaired samples as test statistics, and propose a procedure to find the optimal mixture that minimizes the conditional variances of the test statistics, given the observations. Simulations are conducted for numerical power comparisons between the proposed permutation tests and other existing methods. We apply the proposed method to find differentially expressed genes for a colorectal cancer study. [Copyright &y& Elsevier]

Abstract: A row (or column) of an matrix complies with Regular Minimality (RM) if it has a unique minimum entry which is also a unique minimum entry in its column (respectively, row). The number of violations of RM in a matrix is defined as the number of rows (equivalently, columns) that do not comply with RM. We derive a formula for the proportion of matrices with a given number of violations of RM among all matrices with no tied entries. The proportion of matrices with no more than a given number of violations can be treated as the -value of a permutation test whose null hypothesis states that all permutations of the entries of a matrix without ties are equiprobable, and the alternative hypothesis states that RM violations occur with lower probability than predicted by the null hypothesis. A matrix with ties is treated as being represented by all matrices without ties that have the same set of strict inequalities among their entries. [Copyright &y& Elsevier]

Abstract: Generalized additive models (GAMs) have distinct advantages over generalized linear models as they allow investigators to make inferences about associations between outcomes and predictors without placing parametric restrictions on the associations. The variable of interest is often smoothed using a locally weighted scatterplot smoothing (LOESS) and the optimal span (degree of smoothing) can be determined by minimizing the Akaike Information Criterion (AIC). A natural hypothesis when using GAMs is to test whether the smoothing term is necessary or if a simpler model would suffice. The statistic of interest is the difference in deviances between models including and excluding the smoothed term. As approximate chi-square tests of this hypothesis are known to be biased, permutation tests are a reasonable alternative. We compare the type I error rates of the chi-square test and of three permutation test methods using synthetic data generated under the null hypothesis. In each permutation method a distribution of differences in deviances is obtained from 999 permuted datasets and the null hypothesis is rejected if the observed statistic falls in the upper 5% of the distribution. One test is a conditional permutation test using the optimal span size for the observed data; this span size is held constant for all permutations. This test is shown to have an inflated type I error rate. Alternatively, the span size can be fixed a priori such that the span selection technique is not reliant on the observed data. This test is shown to be unbiased; however, the choice of span size is not clear. A third method is an unconditional permutation test where the optimal span size is selected for observed and permuted datasets. This test is unbiased though computationally intensive. [Copyright &y& Elsevier]

Abstract: The ANOVA method and permutation tests, two heritages of Fisher, have been extensively studied. Several permutation strategies have been proposed by others to obtain a distribution-free test for factors in a fixed effect ANOVA (i.e., single error term ANOVA). The resulting tests are either approximate or exact. However, there exists no universal exact permutation test which can be applied to an arbitrary design to test a desired factor. An exact permutation strategy applicable to fixed effect analysis of variance is presented. The proposed method can be used to test any factor, even in the presence of higher-order interactions. In addition, the method has the advantage of being applicable in unbalanced designs (all-cell-filled), which is a very common situation in practice, and it is the first method with this capability. Simulation studies show that the proposed method has an actual level which stays remarkably close to the nominal level, and its power is always competitive. This is the case even with very small datasets, strongly unbalanced designs and non-Gaussian errors. No other competitor show such an enviable behavior. [Copyright &y& Elsevier]

Abstract: Multiple testing procedures are frequently applied to biomedical and genomic research, for instance, identification of differentially expressed genes in microarray experiments. Resampling methods are commonly used to compute adjusted -values in multiple hypothesis testing problems. Importantly, the resampling-based multiple testing procedures are sensitive to the number of permutations, especially for the MinP adjustment procedure. The single-step MinP adjusted -values are derived from the distribution of the minimum of the -values. Because of computational complexity, the adjusted -values are often computed using the distribution of the maximum of the test statistics (MaxT). This paper proposes an approach based on the kernel density estimation (KDE) technique to reduce the number of permutations for implementing the single-step MinP adjustment. Simulation studies are conducted to demonstrate that the KDE method is more powerful than the MinP adjustment method under independent and correlated models. The three resampling-based single-step adjustment procedures, MaxT, MinP, and KDE, are applied to two published microarray data sets, the colon tumor data set consisting of 40 tumor and 22 normal colon tissue samples on 2000 human genes (endpoints) and the leukemia data set consisting of 27 acute lymphoblastic leukemia and 11 acute myeloid leukemia samples on 3051 genes. The MaxT adjusted -values are very robust to the number of permutations. The MaxT adjusted -values are stable with 10,000 permutations, while the MinP adjusted -values are step functions. As the number of permutations increases, the number of ties decrease. The adjusted -values are stable with 500,000 permutations. For the KDE method, the adjusted -values are stable at 50,000 permutations. At 1000,000 permutations, the three procedures have similar adjusted -values. [Copyright &y& Elsevier]

Abstract: A permutation solution to the problem of genetic differentiation is presented. The focus is on determining whether there are any differences between two populations. The ability to obtain plausible genetic heterogeneities by combining the information of several loci differs depending on the method used, so no statistical test uniformly dominates the others. The procedure proposed here is robust and flexible with regard to the possible configurations of the global alternative hypothesis. Moreover, such a procedure guarantees the rejection of the global hypothesis with probability when all null (local) hypotheses are true. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a modification of Rosenberger and Rukhin''s (Nonparametric Statist. 15 (2003) 455–465) linear rank test following truncated binomial randomization. This modified test is asymptotically normal under much less strict conditions, and unlike Rosenberger and Rukhin''s, can be used with standard score functions. [Copyright &y& Elsevier]

The novel nonparametric two-sample test proposed by Baumgartner et al. (Biometrics 54 (1998) 1129) was derived under a continuous distributional assumption. In practice, however, ties often occur. Since the Baumgartner et al. original test, that is, the test based on the asymptotic distribution of the novel test statistic B, does not control the type I error rate in case of discontinuous distributions, it is recommended an exact permutation test be performed with the statistic B. The resultant test has, according to simulation results, a less conservative size and is more powerful than both the Wilcoxon rank sum test and the Kolmogorov–Smirnov test. The comparison between the exact test based on B and the χ2 test does not show a clear winner, but the new test can be used irrespective of the number of ties occur since no subjective step of binning the data is required. [Copyright &y& Elsevier]

A nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor is consistent in the sense that it tends to infinity under the alternative, and zero under the null. A p -value is then obtained through a permutation test based on the observed Bayes factor. Through a series of simulation studies, the performance of the proposed approach is examined and compared to several existing approaches based on the power of the test as well as the observed Bayes factor. Lastly, the proposed method is applied to a set of real data in ecology. [ABSTRACT FROM AUTHOR]

We use the ideas of maximum mean discrepancy and ranks of nearest neighbors to propose some tests of independence among multiple random vectors of arbitrary dimensions. Numerical studies demonstrate that proposed tests can outperform the existing tests in various examples. [ABSTRACT FROM AUTHOR]

In the framework of Object Oriented Data Analysis, a permutation approach to the two-sample testing problem for network-valued data is proposed. In detail, the present framework proceeds in four steps: (i) matrix representation of the networks, (ii) computation of the matrix of pairwise (inter-point) distances, (iii) computation of test statistics based on inter-point distances and (iv) embedding of the test statistics within a permutation test. The proposed testing procedures are proven to be exact for every finite sample size and consistent. Two new test statistics based on inter-point distances (i.e., IP-Student and IP-Fisher) are defined and a method to combine them to get a further inferential tool (i.e., IP-StudentFisher) is introduced. Simulated data shows that tests with our statistic exhibit a statistical power that is either the best or second-best but very close to the best on a variety of possible alternatives hypotheses and other statistics. A second simulation study that aims at better understanding which features are captured by specific combinations of matrix representations and distances is presented. Finally, a case study on mobility networks in the city of Milan is carried out. The proposed framework is fully implemented in the R package nevada (NEtwork-VAlued Data Analysis). [ABSTRACT FROM AUTHOR]

If the survival function of a random variable X lies to the right of the survival function of a random variable Y , then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y , dominance of Y over X , or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual's willingness to pay for a given environmental improvement. • We suggest four-decision tests for stochastic dominance suitable for paired samples. • The tests are permutation-based and do not rely on distributional assumptions. • A simulation study indicates good power and control of false-detection errors. • The proposed methods are applied to data from a psychophysical experiment. [ABSTRACT FROM AUTHOR]