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Abstract: Consider clustered matched-pair studies for non-inferiority where clusters are independent but units in a cluster are correlated. An inexpensive new procedure and the expensive standard one are applied to each unit and outcomes are binary responses. Appropriate statistics testing non-inferiority of a new procedure have been developed recently by several investigators. In this paper, we investigate power and sample size requirement of the clustered matched-pair study for non-inferiority. Power of a test is related primarily to the number of clusters. The effect of a cluster size on power is secondary. The efficiency of a clustered matched-pair design is inversely related to the intra-class correlation coefficient within a cluster. We present an explicit formula for obtaining the number of clusters for a given cluster size and the cluster size for a given number of clusters for a specific power. We also provide alternative sample size calculations when available information regarding parameters are limited. The formulas can be useful in designing a clustered matched-pair study for non-inferiority. An example for determining sample size to establish non-inferiority for a clustered matched-pair study is illustrated. [Copyright &y& Elsevier]

Abstract: Many studies in biomedical fields are carried out using diagnoses reported by different raters to evaluate the agreement of multiple ratings. The most popular indices of agreement are kappa measures including Cohen’s kappa and weighted kappa for binary and ordinal outcomes, respectively. However, when raters assess the same observation on two or more occasions, these ratings are dependent and so the correlation between kappa estimates must be considered when making inferences. In this paper, we focus on testing the equality of correlated kappa coefficients using the generalized estimating equation (GEE) approach and applying quasi-likelihood under the independence model criterion (QIC) measures for model selection. Simulation studies are conducted to compare the performance between GEE with and without QIC measures, weighted least squares (WLS) and independence approaches for binary and ordinal data. Two applications are illustrated: a comparison of two methods for assessing cervical ectopy, and similarity in myopic status for monozygous twins and dizygous twins. We conclude that when performing the QIC model-selection procedure in GEE models and taking into account the correlation between kappa measures, it leads to nominal type I errors and larger powers. [Copyright &y& Elsevier]

Abstract: Statistical practice often requires combining evidence from independent sources. A popular approach is to combine p-values. Motivated by the observation that p-values under the alternative are stochastically smaller than p-values under the null, we develop new combination rules that explicitly account for this ordering. The new combination rules are broadly applicable, optimal against some alternatives, and highly efficient against optimal procedures. [Copyright &y& Elsevier]

Abstract: In a two-sample location-scale model with censored data, the logrank test is asymptotically efficient when the error distribution is extreme minimum value. On the other hand, the Wilcoxon test is asymptotically efficient when the error distribution is logistic. We propose a pretest for choosing between logrank and Wilcoxon by determining if the error distribution is closer to extreme minimum value or logistic. This adaptive test is compared with the logrank and Wilcoxon tests through simulation. [Copyright &y& Elsevier]

Abstract: The Satorra Bentler (SB) and the Browne ADF chi-square statistics are used for testing structural equation models with non-normal data. The relationships between the SB and ADF statistics and kurtosis are developed and it is shown that the weighted deviations of the “population” true second-order moments and the fitted second-order moments for these statistics tend to decrease with increasing kurtosis if the model does not hold. The results predict that high kurtosis can lead to loss of power. The results are obtained without simulation. [Copyright &y& Elsevier]

Abstract: The two-parameter Birnbaum–Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum–Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum–Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. [Copyright &y& Elsevier]

Abstract: When high dimensional microarray data is given, it is of interest to select significant genes by controlling a given level of Type-I error. One popular way to control the level is the false discovery rate (FDR). This paper considers gene selection based on the local false discovery rate. In most of the previous studies, the null distribution of gene expression is commonly assumed to be a normal distribution. However, if the null distribution has heavier tail than that of normal, there may exist too many false discoveries leading to the failure of controlling the given level of FDR. We propose a novel procedure which enriches a class of null distribution based on a mixture of normals. We present simulation studies to show that our proposed procedure is less sensitive to variation of null distribution than local false discovery rate with a single normal for the null. We also provide real example of gene expression profiles of antigen-specific human CD8+ T-lymphocytes treated with cytokine Interleukin-2 (IL-2) and Interleukin-15 (IL-15) for comparison. [Copyright &y& Elsevier]

Abstract: In this paper, a data-driven test is proposed to compare two independent or dependent stationary time series, in terms of the second order dynamics. We show that the problem of time series comparison is equivalent to a goodness-of-fit test checking if a constant model is adequate. Using the same framework, the proposed test is easily extended to compare multiple time series and time series of different lengths. Different to previous methods, it is based on generalized score statistics in an estimating equation setting, with some weak and flexible conditions. An extensive simulation study illustrates the validity of the asymptotic result and finite sample properties, using the tapered periodogram. The proposed test is found to perform well for many different situations, including time series with heavy-tailed or skewed innovations. An application to damage detection using vibration data is discussed. [Copyright &y& Elsevier]

Abstract: We propose a new approach, the forward functional testing (FFT) procedure, to cluster number selection for functional data clustering. We present a framework of subspace projected functional data clustering based on the functional multiplicative random-effects model, and propose to perform functional hypothesis tests on equivalence of cluster structures to identify the number of clusters. The aim is to find the maximum number of distinctive clusters while retaining significant differences between cluster structures. The null hypotheses comprise equalities between the cluster mean functions and between the sets of cluster eigenfunctions of the covariance kernels. Bootstrap resampling methods are developed to construct reference distributions of the derived test statistics. We compare several other cluster number selection criteria, extended from methods of multivariate data, with the proposed FFT procedure. The performance of the proposed approaches is examined by simulation studies, with applications to clustering gene expression profiles. [Copyright &y& Elsevier]

Abstract: While parametric copulas often lack expressive capacity to capture the complex dependencies that are usually found in empirical data, non-parametric copulas can have poor generalization performance because of overfitting. A semiparametric copula method based on the family of bivariate Archimedean copulas is introduced as an intermediate approach that aims to provide both accurate and robust fits. The Archimedean copula is expressed in terms of a latent function that can be readily represented using a basis of natural cubic splines. The model parameters are determined by maximizing the sum of the log-likelihood and a term that penalizes non-smooth solutions. The performance of the semiparametric estimator is analyzed in experiments with simulated and real-world data, and compared to other methods for copula estimation: three parametric copula models, two semiparametric estimators of Archimedean copulas previously introduced in the literature, two flexible copula methods based on Gaussian kernels and mixtures of Gaussians and finally, standard parametric Archimedean copulas. The good overall performance of the proposed semiparametric Archimedean approach confirms the capacity of this method to capture complex dependencies in the data while avoiding overfitting. [Copyright &y& Elsevier]

Abstract: To test the hypothesis of symmetry about an unknown median we propose the maximum of a partial sum process based on ranked set samples. We discuss the properties of the test statistic and investigate a modified bootstrap ranked set sample bootstrap procedure to obtain its sampling distribution. The power of the new test statistic is compared with two existing tests in a simulation study. [ABSTRACT FROM AUTHOR]

Abstract: We aim to construct suitable tests when we have imprecise information about a sample. More specifically, we assume that we get a collection of n sets of values, each one characterizing an imprecise measurement. Each set specifies where the true sample value is (and where it is not) with full confidence, but it does not provide any additional information. Our main objectives are twofold: first we will review different kinds of tests in the literature about inferential statistics with random sets and discuss the approach that best suits our definition of imprecise data. Secondly, we will show that we can take advantage from mark and recapture techniques to improve the accuracy of our decisions. These techniques will be specially important when the population is small enough (with respect to the sample size) that recaptures are common. They also seem to be useful when resampling techniques are involved in the decision process. [ABSTRACT FROM AUTHOR]

Abstract: In some applications involving comparison of treatment means, it is known a priori that population means are ordered in a certain way. In such situations, imposing constraints on the treatment means can greatly increase the effectiveness of statistical procedures. This paper proposes a unified Bayesian method which performs a simultaneous comparison of treatment means and parameter estimation in ANOVA models with order constraints on the means. A continuous prior restricted to order constraints is employed, and posterior samples of parameters are generated using a Markov chain Monte Carlo method. Posterior probabilities of all possible hypotheses on the equality/inequality of treatment means are obtained using Savage–Dickey density ratios, for which we propose a simple and computationally efficient estimation method. Posterior densities and HPD intervals of parameters of interest are estimated with almost no extra cost, given some by-products from the test procedure. Simulation study results show that the proposed method outperforms the test without constraints and that the method is powerful in detecting the true hypothesis. The method is applied to the ramus bone sizes of 20 boys, which were measured at four time points. The proposed Bayesian test reveals that there are two growth spurts in the ramus bone size during the observed period, which could not be detected by pairwise comparisons of the means. [Copyright &y& Elsevier]

Abstract: Controlling the false discovery rate (FDR) is a powerful approach to deal with a large number of hypothesis tests, such as in gene expression data analyses and genome-wide association studies. To further boost power, here we propose a floating prioritized subset analysis (floating PSA) that can more effectively use prior knowledge and detect more genes that are differentially expressed. Genes are first allocated into two subsets: a prioritized subset and a non-prioritized subset, according to investigators’ prior biological knowledge. We allow the FDRs of the two subsets to vary freely (to float) but aim to control the overall FDR at a desired level. An algorithm for the floating PSA is developed to detect the largest number of true positives. Theoretical justifications of the algorithm are given, and computer simulation studies show that the method has good statistical properties. We apply this method to detect genes that are differentially expressed between acute lymphoblastic leukemia and acute myeloid leukemia patients. The result shows that our floating PSA identifies 32 more genes (permutation-based FDR=0.0427) than the conventional (fixed) FDR control. Another example is a colon cancer study, and our floating PSA identifies 43 more genes (permutation-based FDR=0.0502). The floating PSA method is to be recommended for the detection of differentially expressed genes, in light of its power, robustness, and ease of implementation. [Copyright &y& Elsevier]

Abstract: The problem of identifying differentially expressed genes is considered in a microarray experiment. This motivates us to involve an appropriate multiple testing setup to high dimensional and low sample size testing problems in highly nonstandard setups. Family-wise error rate (FWER) is too conservative to control the type I error, whereas a less conservative false discovery rate has received considerable attention in a wide variety of research areas such as genomics and large biological systems. Recently, a less conservative method than FDR, the -FDR, which generalizes the FDR has been proposed by . Most of the current FDR procedures assume restrictive dependence structures, resulting in being less reliable. The purpose of this paper is to address these very large multiplicity problems by adopting a proposed -FDR controlling procedure under suitable dependence structures and based on a Poisson distributional approximation in a unified framework. We compare the performance of the proposed -FDR procedure with that of other FDR controlling procedures, with an illustration of the leukemia microarray study of and simulated data. For power consideration, different FDR procedures are assessed using false negative rate (FNR). An unbiased property is appraised by and a higher value of . The proposed -FDR procedure is characterized by greater power without much elevation of -FDR. [Copyright &y& Elsevier]

Abstract: A studentized range test is proposed to test the hypothesis of average equivalence of treatments in terms of the distance between means against the alternative hypothesis of inequivalence. A least favorable configuration (LFC) of means to guarantee the maximum level at a null hypothesis and a LFC of means to guarantee the minimum power at an alternative hypothesis are obtained. The level and power of the test are fully independent of the unknown means and variances. For a given level and a given power, the critical value and the required sample size for an experiment can be simultaneously determined, and the tables of critical values and sample sizes are provided for practitioners. A real numerical example to demonstrate the use of the test procedure is provided. In situations where the common population variance is unknown and the equivalence is the actual distance between means without standardization, a two-stage sampling procedure can be employed to find these solutions. It proves to be a quite feasible solution for practitioners. [Copyright &y& Elsevier]

Abstract: Power and sample size determination has been a challenging issue for multiple testing procedures, especially stepwise procedures, mainly because (1) there are several power definitions, (2) power calculation usually requires multivariate integration involving order statistics, and (3) expansion of these power expressions in terms of ordinary statistics, instead of order statistics, is generally a difficult task. Traditionally power and sample size calculations rely on either simulations or some recursive algorithm; neither is straightforward and computationally economic. In this paper we develop explicit formulas for minimal power and -power of stepwise procedures as well as complete power of single-step procedures for exchangeable and non-exchangeable bivariate and trivariate test statistics. With the explicit power expressions, we were able to directly calculate the desired power, given sample size and correlation. Numerical examples are presented to illustrate the relationship among power, sample size and correlation. [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: We consider the problem of dichotomizing a continuous covariate when performing a regression analysis based on a generalized estimation approach. The problem involves estimation of the cutpoint for the covariate and testing the hypothesis that the binary covariate constructed from the continuous covariate has a significant impact on the outcome. Due to the multiple testing used to find the optimal cutpoint, we need to make an adjustment to the usual significance test to preserve the type-I error rates. We illustrate the techniques on one data set of patients given unrelated hematopoietic stem cell transplantation. Here the question is whether the CD34 cell dose given to patient affects the outcome of the transplant and what is the smallest cell dose which is needed for good outcomes. [Copyright &y& Elsevier]

Abstract: Item response theory is one of the modern test theories with applications in educational and psychological testing. Recent developments made it possible to characterize some desired properties in terms of a collection of manifest ones, so that hypothesis tests on these traits can, in principle, be performed. But the existing test methodology is based on asymptotic approximation, which is impractical in most applications since the required sample sizes are often unrealistically huge. To overcome this problem, a class of tests is proposed for making exact statistical inference about four manifest properties: covariances given the sum are non-positive (CSN), manifest monotonicity (MM), conditional association (CA), and vanishing conditional dependence (VCD). One major advantage is that these exact tests do not require large sample sizes. As a result, tests for CSN and MM can be routinely performed in empirical studies. For testing CA and VCD, the exact methods are still impractical in most applications, due to the unusually large number of parameters to be tested. However, exact methods are still derived for them as an exploration toward practicality. Some numerical examples with applications of the exact tests for CSN and MM are provided. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problem of testing uniform association in cross-classifications having ordered categories, taking as test statistic one in the family proposed by Conde and Salicrú [J. Conde, M. Salicrú, Uniform association in contingency tables associated to Csiszár divergence, Statistics and Probability Letters 37 (1998) 149–154]. We consider two approximations to the null distribution of the test statistics in this family: an estimation of the asymptotic null distribution and a bootstrap estimator. We prove that both approximations are asymptotically equivalent. To study their finite sample performance, we carried out two simulation experiments, whose results are presented. From the simulations it can be concluded that the bootstrap estimator behaves much better than the estimated asymptotic null distribution. [Copyright &y& Elsevier]

The article offers information on how to improve the performance of a process in a company. The process improvement program is compared with learning how to ride a bicycle. It states that like a first time bike learner is taught to ride on a simple bike, same way the managers should be taught about the process improvement program through simple statistical models and not include sophisticated improvement programs like analysis of variance (AOV) and statistical process control (SPC). An A3 report used for the process improvement program by Toyota Motor Corp. is also presented in the article. The A3 report is a simple model of problem solving on paper which focuses on problem, its analyzes, offers solution and implements the solution for the problem.

Abstract: We introduce a bootstrap procedure to test the hypothesis that variances are homogeneous. The procedure uses a variance-based statistic, and is derived from a normal-theory test for equality of variances. The test equivalently expressed the hypothesis as , where ’s are log contrasts of the population variances. A box-type acceptance region is constructed to test the hypothesis . Simulation results indicated that our method is generally superior to the Shoemaker and Levene tests, and the bootstrapped version of the Levene test in controlling the Type I and Type II errors. [Copyright &y& Elsevier]

Abstract: Nonparametric tests for the null hypothesis that a function has a prescribed form are developed and applied to data sets with missing observations. Omnibus nonparametric tests such as the order selection tests, do not need to specify a particular alternative parametric form, and have power against a large range of alternatives. More specifically, likelihood-based order selection tests are defined that can be used for multiply imputed data when the data are missing-at-random. A simulation study and data analysis illustrate the performance of the tests. In addition, an Akaike information criterion for model selection is presented that can be used with multiply imputed datasets. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm to segment synthetic aperture radar (SAR) images, corrupted by speckle noise. Most standard segmentation techniques may require speckle filtering previously. Our approach performs radar image segmentation using the original noisy pixels as input data, i.e. without any preprocessing step. The algorithm includes a statistical region growing procedure combined with hierarchical region merging. The region growing step oversegments the input radar image, thus enabling region aggregation by employing a combination of the Kolmogorov–Smirnov (KS) test with a hierarchical stepwise optimization (HSWO) algorithm for performance improvement. We have tested and assessed the proposed technique on artificially speckled image and real SAR data. [Copyright &y& Elsevier]

Abstract: An encompassing prior (EP) approach to facilitate Bayesian model selection for nested models with inequality constraints has been previously proposed. In this approach, samples are drawn from the prior and posterior distributions of an encompassing model that contains an inequality restricted version as a special case. The Bayes factor in favor of the inequality restriction then simplifies to the ratio of the proportions of posterior and prior samples consistent with the inequality restriction. This formalism has been applied almost exclusively to models with inequality or “about equality” constraints. It is shown that the EP approach naturally extends to exact equality constraints by considering the ratio of the heights for the posterior and prior distributions at the point that is subject to test (i.e., the Savage–Dickey density ratio). The EP approach generalizes the Savage–Dickey ratio method, and can accommodate both inequality and exact equality constraints. The general EP approach is found to be a computationally efficient procedure to calculate Bayes factors for nested models. However, the EP approach to exact equality constraints is vulnerable to the Borel–Kolmogorov paradox, the consequences of which warrant careful consideration. [Copyright &y& Elsevier]

Abstract: A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distribution-free, with critical values that are already tabulated. The smooth tests are shown to be optimal in a semiparametric sense discussed in the paper, and they are robust to conditional heteroscedasticity of unknown form. A simulation study shows that the data-driven smooth tests perform very well for a wide range of realistic alternatives and have more power than omnibus and other competing tests. Finally, an application to the S&P 500 stock index and some of its components highlights the merits of our approach. The paper also contains a new weak convergence theorem that is of independent interest. [Copyright &y& Elsevier]

Abstract: The several sample case of the so-called nonparametric Behrens–Fisher problem in repeated measures designs is considered. That is, even under the null hypothesis, the marginal distribution functions in the different groups may have different shapes, and are not assumed to be equal. Moreover, the continuity of the marginal distribution functions is not required so that data with ties and, particularly, ordered categorical data are covered by this model. A multiple relative treatment effect is defined which can be estimated by using the mid-ranks of the observations within pairwise samples. The asymptotic distribution of this estimator is derived, along with a consistent estimator of its asymptotic covariance matrix. In addition, a multiple contrast test and related simultaneous confidence intervals for the relative marginal effects are derived and compared to rank-based Wald-type and ANOVA-type statistics. Simulations show that the ANOVA-type statistic and the multiple contrast test appear to maintain the pre-assigned level of the test quite accurately (even for rather small sample sizes) while the Wald-type statistic leads, as expected, to somewhat liberal decisions. Regarding the power, none of the statistics is uniformly superior. A real data set illustrates the application. [Copyright &y& Elsevier]

Abstract: Switching regression models form a suitable model class for regression problems with unobserved heterogeneity. A basic issue encountered in applications of switching regression models is to choose the number of states of the switching regime. Based on the modified likelihood ratio test (LRT) statistic a test for two against more states of the regime is proposed, and its asymptotic distribution is derived in the case when there is a single switching parameter. Further, it is shown that the asymptotic distribution of the test remains unchanged if the regime is Markov dependent. A simulation study illustrates the finite-sample behavior of the test. Finally, the methodology is applied to the data of a dental health trial. In this case the model selection criteria AIC and BIC favor distinct binomial regression models with switching intercepts (AIC three states, BIC two states). The modified LRT allows us to reject the null hypothesis of two states in favor of three states. [Copyright &y& Elsevier]

Abstract: Mutation operators such as Gaussian, Lévy and Cauchy have been used with evolutionary programming (EP). According to the no free lunch theorem, it is impossible for EP with a single mutation operator to outperform always. For example, Classical EP (CEP) with Gaussian mutation is better at searching in a local neighborhood while the Fast EP (FEP) with the Cauchy mutation performs better over a larger neighborhood. Motivated by these observations, we propose an ensemble approach where each mutation operator has its associated population and every population benefits from every function call. This approach enables us to benefit from different mutation operators with different parameter values whenever they are effective during different stages of the search process. In addition, the recently proposed Adaptive EP (AEP) using Gaussian (ACEP) and Cauchy (AFEP) mutations is also evaluated. In the AEP, the strategy parameter values are adapted based on the search performance in the previous few generations. The performance of ensemble is compared with a mixed mutation strategy, which integrates several mutation operators into a single algorithm as well as against the AEP with a single mutation operator. Improved performance of the ensemble over the single mutation-based algorithms and mixed mutation algorithm is verified using statistical tests. [Copyright &y& Elsevier]

The article discusses statistics, which is a branch of applied mathematics that seeks to draw inferences from limited, incomplete, or imperfect data. The focus of the article is the various ways in which statisticians can reuse data to quantify the uncertainty of complex models. An overview of statistics is presented which includes a discussion on how statistical inference is used to estimate a given parameter, or to test a hypothesis related to them, and various origin myths of probability distributions, such as the origin of the Gaussian bell curve. Also discussed are fitting models, in which statisticians record a lot of data and fit it into an appropriate model, and bootstrapping, which approximates a sampling distribution with three sources of approximation errors.

Abstract: This note is motivated by recent works of and . Herein, we simplify the score statistic presented by to test overdispersion in the zero-inflated generalized Poisson (ZIGP) mixed model, and discuss an extension to test overdispersion in zero-inflated Poisson (ZIP) mixed models. Examples highlight the application of the extended results. The extensive simulation study for testing overdispersion in the Poisson mixed model indicates that the proposed score statistics maintain the nominal level reasonably well. In practice, the appropriate model is chosen based on the approximate mean–variance relationship in the data, and a formal score test based on asymptotic standard normal distribution can be employed for testing overdispersion. A case study is provided to illustrate procedures for data analysis. [Copyright &y& Elsevier]

Abstract: In this paper we propose GP-COACH, a Genetic Programming-based method for the learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems. GP-COACH learns disjunctive normal form rules (generated by means of a context-free grammar) coded as one rule per tree. The population constitutes the rule base, so it is a genetic cooperative-competitive learning approach. GP-COACH uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules. The results obtained have been validated by the use of non-parametric statistical tests, showing a good performance in terms of accuracy and interpretability. [Copyright &y& Elsevier]

Abstract: This paper presents procedures for hypothesis testing and interval estimation for the common mean of several inverse Gaussian populations when the scalar parameters are unknown and unequal. The proposed approaches are hybrids between the generalized inference method and the large-sample theory. Some simulation results are presented to compare the performance of the proposed approaches with that of the existing approach. The simulation results indicate that one of the proposed approaches performs better than the existing approach in most cases. Furthermore, our approaches can be simply carried out by a few simulation steps. Finally, the proposed approaches are illustrated by using three examples. [Copyright &y& Elsevier]

An essay is presented on the use of statistics in science and the shortcomings associated with the practice. The author asserts that the so-called scientific method that involves statistical hypothesis testing is unsound. Also noted is the tendency to misunderstand statistical test results. The author believes that studies correlating genetics and disease have the most problems associated with statistical interpretations. INSET: Statistical criticisms.

Abstract: The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes a decision of abstaining. This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model. The results enrich the rough set theory by ideas from Bayesian decision theory and hypothesis testing in statistics. The connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications. [Copyright &y& Elsevier]

Abstract: The likelihood approach based on the empirical distribution functions is a well-accepted statistical tool for testing. However, the proof schemes of the Neyman–Pearson type lemmas induce consideration of density-based likelihood ratios to obtain powerful test statistics. In this article, we introduce the distribution-free density-based likelihood technique, applied to test for goodness-of-fit. We focus on tests for normality and uniformity, which are common tasks in applied studies. The well-known goodness-of-fit tests based on sample entropy are shown to be a product of the proposed empirical likelihood (EL) methodology. Although the efficiency of test statistics based on classes of entropy estimators has been widely addressed in the statistical literature, estimation of the sample entropy has been not invariantly defined, and hence this estimation produces tests that are difficult to be applied to real data studies. The proposed EL approach defines clear forms of the entropy-based tests. Monte Carlo simulation results confirm the preference of the proposed method from a power perspective. Real data examples study the proposed approach in practice. [Copyright &y& Elsevier]

Abstract: Time series of counts are commonly observed in real-world applications. The integer-valued ARCH models are able to describe integer-valued processes and offer the potential to be widely applied in practice in future. This paper develops an asymptotic theory for (partial) autocorrelations of the conditional residuals from the integer-valued ARCH model. Based on the above results, we propose five portmanteau test statistics, which are very useful in checking the adequacy of a fitted integer-valued ARCH specification. The asymptotic distributions of the statistics are derived and their finite sample properties are studied in detail through Monte Carlo simulations. Finally, we illustrate the results analyzing two empirical examples. [Copyright &y& Elsevier]

Abstract: We develop a Bayesian approach to sample size and power calculations for cross-sectional studies that are designed to evaluate and compare continuous medical tests. For studies that involve one test or two conditionally independent or dependent tests, we present methods that are applicable when the true disease status of sampled individuals will be available and when it will not. Within a hypothesis testing framework, we consider the goal of demonstrating that a medical test has area under the receiver operating characteristic (ROC) curve that exceeds a minimum acceptable level or another relevant threshold, and the goals of establishing the superiority or equivalence of one test relative to another. A Bayesian average power criterion is used to determine a sample size that will yield high posterior probability, on average, of a future study correctly deciding in favor of these goals. The impacts on Bayesian average power of prior distributions, the proportion of diseased subjects in the study, and correlation among tests are investigated through simulation. The computational algorithm we develop involves simulating multiple data sets that are fit with Bayesian models using Gibbs sampling, and is executed by using WinBUGS in tandem with R. [Copyright &y& Elsevier]

Abstract: Goodness-of-fit tests are constructed for the two-parameter Birnbaum–Saunders distribution in the case where the parameters are unknown and are therefore estimated from the data. With each test the procedure starts by computing efficient estimators of the parameters. Then the data are transformed to normality and normality tests are applied on the transformed data, thereby avoiding reliance on parametric asymptotic critical values or the need for bootstrap computations. Two classes of tests are considered, the first class being the classical tests based on the empirical distribution function, while the other class utilizes the empirical characteristic function. All methods are extended to cover the case of generalized three-parameter Birnbaum–Saunders distributions. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a Portmanteau-type test of randomness for symmetric stable random variables with exponent , using a test statistic that differs from, but has the same general form as Box–Pierce Q-statistic, which is defined using the codifference function. We obtain that unlike a similar test proposed in [Runde, R., 1997. The asymptotic null distribution of the Box–Pierce Q-statistic for random variables with infinite variance—with an application to German stock returns. Journal of Econometrics 78, 205–216], the asymptotic distribution of the proposed statistic is similar to the classical case, that is asymptotically distributed, both in finite and infinite variance cases. Simulation studies are performed to obtain the small sample performance of the proposed statistic. We found that the proposed statistic works fairly well, in the sense that in the infinite variance case, under suitable choice of the design parameter, its empirical levels are closer to the theoretical ones than Runde’s statistic. In the finite variance case, its empirical level is approximately the same as that of Ljung–Box’s statistic [Ljung, G.M. and Box, G.E.P., 1978. On a measure of lack of fit in time series models. Biometrika 65, 297–303]. Furthermore, the statistic also has good power against the AR(1) alternative. We provide an empirical example using some stocks chosen from the LQ45 index listed in the Indonesia Stock Exchange (IDX). [Copyright &y& Elsevier]

Abstract: In this paper we propose a new class of spatial concentration measures to verify hypotheses on the spatial concentration of empirical phenomena. Our proposed measures incorporate the ideas of both a-spatial concentration and spatial autocorrelation. We discuss many issues related to the approximate sampling theory and we suggest a Monte Carlo test for the presence of significant spatial concentration. A simulation experiment studying the relationship of the new measure to different spatial patterns and to different levels of a-spatial variability is also reported. A discussion related to irregular space is included. [Copyright &y& Elsevier]

Abstract: This paper studies the finite sample performance of the sieve bootstrap augmented Dickey-Fuller (ADF) unit root test. It is well known that this test’s accuracy in terms of rejection probability under the null depends greatly on the underlying DGP. Through extensive simulations, we find that it also depends on the number of lags employed in the bootstrap DGP and in the bootstrap ADF regression. Based on this finding and using some well established theoretical results, we propose a simple modification that significantly improves the test’s accuracy. We also introduce different versions of the fast double bootstrap, each modified according to the same theoretical basis. According to our simulations, these new testing procedures have lower error in rejection probability under the null while retaining good power. [Copyright &y& Elsevier]

Abstract: In this paper we compare the size distortions and powers for Pearson’s -statistic, likelihood ratio statistic , score statistic and two statistics, which we call and here, proposed by [Potthoff, R.F., Whittinghill, M., 1966. Testing for homogeneity: II. The Poisson distribution. Biometrika 53, 183–190] for testing the equality of the rates of Poisson processes. Asymptotic tests and parametric bootstrap tests are considered. It is found that the asymptotic test is too conservative to be recommended, while the other four asymptotic tests perform similarly and their powers are close to those of their parametric bootstrap counterparts when the observed counts are large enough. When the observed counts are not large, Monte Carlo simulation suggested that the asymptotic test using , and statistics are discouraged; none of the parametric bootstrap tests with the five statistics considered here is uniformly best or worst, and the asymptotic tests using Pearson’s and always have similar powers to their bootstrap counterparts. Thus, the asymptotic Pearson’s and tests have an advantage over all five parametric bootstrap tests in terms of their computational simplicity and convenience, and over the other four asymptotic tests in terms of their powers and size distortions. [Copyright &y& Elsevier]

Abstract: Hierarchical clustering is a common procedure for identifying structure in a dataset, and this is frequently used for organizing genomic data. Although more advanced clustering algorithms are available, the simplicity and visual appeal of hierarchical clustering have made it ubiquitous in gene expression data analysis. Hence, even minor improvements in this framework would have significant impact. There is currently no simple and systematic way of assessing and displaying the significance of various clusters in a resulting dendrogram without making certain distributional assumptions or ignoring gene-specific variances. In this work, we introduce a permutation test based on comparing the within-cluster structure of the observed data with those of sample datasets obtained by permuting the cluster membership. We carry out this test at each node of the dendrogram using a statistic derived from the singular value decomposition of variance matrices. The -values thus obtained provide insight into the significance of each cluster division. Given these values, one can also modify the dendrogram by combining non-significant branches. By adjusting the cut-off level of significance for branches, one can produce dendrograms with a desired level of detail for ease of interpretation. We demonstrate the usefulness of this approach by applying it to illustrative datasets. [Copyright &y& Elsevier]

Abstract: A generalization of the nonparametric linear rank statistics is presented to handle the two-group comparison with multiple events. For a sample divided into two groups, in which each subject may experience at least two distinct failures, the logrank tests are extended to test the null hypothesis that the vector of the marginal survival distributions of the first group equals that of the second group. Two cases are distinguished depending on whether the null hypothesis does or does not imply the equality of the joint survival functions. In both cases, under the null hypothesis, the asymptotic joint distribution of the vector of the marginal statistics is shown to be Gaussian with covariance matrix consistently estimated using martingale properties. These theoretical results are illustrated by a simulation study and an application on the German Breast Cancer data. An extension to multiple hypotheses testing in multivariate proportional hazards models is also developed. [Copyright &y& Elsevier]

Abstract: We are interested in testing hypotheses that concern the parameter of a logistic regression model. A robust Wald-type test based on a weighted Bianco and Yohai [ Bianco, A.M., Yohai, V.J., 1996. Robust estimation in the logistic regression model. In: H. Rieder (Ed) Robust Statistics, Data Analysis, and Computer Intensive Methods In: Lecture Notes in Statistics, vol. 109, Springer Verlag, New York, pp. 17–34] estimator, as implemented by Croux and Haesbroeck [Croux, C., Haesbroeck, G., 2003. Implementing the Bianco and Yohai estimator for logistic regression. Computational Statististics and Data Analysis 44, 273–295], is proposed. The asymptotic distribution of the test statistic is derived. We carry out an empirical study to get a further insight into the stability of the -value. Finally, a Monte Carlo study is performed to investigate the stability of both the level and the power of the test, for different choices of the weight function. [Copyright &y& Elsevier]

Abstract: The main purpose of this work is to study the behaviour of Skovgaard’s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3–32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian Journal of Probability and Statistics 19, 13–31]. We show that, for our model, Skovgaard’s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. [Copyright &y& Elsevier]

Abstract: Shapiro and Wilk’s [Shapiro, S.S., Wilk, M.B., 1965. An analysis of variance test for normality (complete samples). Biometrika 52, 591–611] -statistic was found to have competitive power performance in testing univariate normality. Generalizations of the -statistic to the multivariate case have been proposed by many researchers. In this paper, we propose a family of generalized -statistics for testing high-dimensional normality by using the theory of spherical distributions. The proposed statistics apply to the case that the sample size is smaller than the dimension. Monte Carlo studies demonstrate feasible performance of the proposed tests in controlling type I error rates and power against some non-normal data. It is concluded that the proposed statistics are superior to existing generalized-statistics and show competitive benefits in testing high-dimensional normality with small sample size. [Copyright &y& Elsevier]

Abstract: Zero-inflated Poisson (ZIP) regression model is a popular approach to the analysis of count data with excess zeros. For correlated count data where the observations are either repeated or clustered outcomes from individual subjects, ZIP mixed regression model may be appropriate. However, ZIP model may often fail to fit such data either because of over-dispersion or because of under-dispersion in relation to the Poisson distribution. In this paper, we extend the ZIP mixed regression model to zero-inflated generalized Poisson (ZIGP) mixed regression model, where the base-line discrete distribution is generalized Poisson (GP) distribution, which is a natural extension of standard Poisson distribution. Furthermore, the random effects are considered in both zero-inflated and GP components throughout the paper. An EM algorithm for estimating parameters is proposed based on the best linear unbiased prediction-type (BLUP) log-likelihood and the residual maximum likelihood (REML). Meanwhile, several score tests are presented for testing the ZIP mixed regression model against the ZIGP mixed regression model, and for testing the significance of regression coefficients in zero-inflation and generalized Poisson portion. A numerical example is given to illustrate our methodology and the properties of score test statistics are investigated through Monte Carlo simulations. [Copyright &y& Elsevier]