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The paper investigates a hypothesis testing problem concerning the potential additional contributions of other covariates to the structural function, given the known covariates. The structural function is the conditional expectation given covariates in which the response may depend on unknown nuisance functions. It includes classic regression functions and the conditional average treatment effects as illustrative instances. Based on Neyman's orthogonality condition, the proposed distance-based test exhibits the quasi-oracle property in the sense that the nuisance function asymptotically does not influence on the limiting distributions of the test statistic under both the null and alternatives. This novel test can effectively detect the local alternatives distinct from the null at the fastest possible rate in hypothesis testing. This is particularly noteworthy given the involvement of nonparametric estimation of the conditional expectation. Numerical studies are conducted to examine the performance of the test. In the real data analysis section, the proposed tests are applied to identify significantly explanatory covariates that are associated with AIDS treatment effects, yielding noteworthy insights. [ABSTRACT FROM AUTHOR]

Abstract Estimation and hypothesis tests for partial linear multiplicative models are considered in this paper. A profile least product relative error estimation method is proposed to estimate unknown parameters. We employ the smoothly clipped absolute deviation penalty to do variable selection. A Wald-type test statistic is proposed to test a hypothesis on parametric components. The asymptotic properties of the estimators and test statistics are established. We also suggest a score-type test statistic for checking the validity of partial linear multiplicative models. The quadratic form of the scaled test statistic has an asymptotic chi-squared distribution under the null hypothesis and follows a non-central chi-squared distribution under local alternatives, converging to the null hypothesis at a parametric convergence rate. We conduct simulation studies to demonstrate the performance of the proposed procedure and a real data is analyzed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

In the age of big data, data integration is a critical step especially in the understanding of how diverse data types work together and work separately. Among data integration methods, the Angle-Based Joint and Individual Variation Explained (AJIVE) approach is particularly attractive because it not only studies joint behavior but also individual behavior. Typically AJIVE scores indicate important relationships between data objects, such as clusters. An important challenge is understanding which features, i.e. variables, are associated with those relationships. This challenge is addressed by the proposal of a hypothesis test for assessing statistical significance of features. The new test is inspired by the related jackstraw method developed for Principal Component Analysis. We use a high-dimensional multi-genomic cancer data set as our strong motivation and deep illustration of the methodology. [ABSTRACT FROM AUTHOR]

We consider estimation and hypothesis test for partial linear measurement errors models when the response variable and covariates in the linear part are measured with additive distortion measurement errors, which are unknown functions of a commonly observable confounding variable. We propose a transformation based profile least squares estimator to estimate unknown parameter under unrestricted and restricted conditions. Asymptotic properties for the estimators are established. To test a hypothesis on the parametric components, a test statistic based on the normalized difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we further show that its limiting distribution is a standard chi-squared distribution. Lastly, we suggest a lack-of-fit test of score type for checking the validity of partial linear models. The quadratic form of the scaled test statistic is asymptotically chi-squared under the null hypothesis and a non-centered one under local alternatives converging to the null hypothesis at parametric rates. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analyzed for an illustration. [ABSTRACT FROM AUTHOR]

In materials science and many other application domains, 3D information can often only be obtained by extrapolating from 2D slices. In topological data analysis, persistence vineyards have emerged as a powerful tool to take into account topological features stretching over several slices. It is illustrated how persistence vineyards can be used to design rigorous statistical hypothesis tests for 3D microstructure models based on data from 2D slices. More precisely, by establishing the asymptotic normality of suitable longitudinal and cross-sectional summary statistics, goodness-of-fit tests that become asymptotically exact in large sampling windows are devised. The testing methodology is illustrated through a detailed simulation study and a prototypical example from materials science is provided. [ABSTRACT FROM AUTHOR]

Based on the random matrix theory, a unified numerical approach is developed for power calculation in the general framework of hypothesis testing with high-dimensional covariance matrices. In the central limit theorem of linear spectral statistics for sample covariance matrices, the theoretical mean and covariance are computed numerically. Based on these numerical values, the power of the hypothesis test can be evaluated, and furthermore the confidence interval for the unknown parameters in the high-dimensional covariance matrix can be constructed. The validity of the proposed algorithms is well supported by a convergence theorem. Our numerical method is assessed by extensive simulation studies, and a real data example of the S & P 100 index data is analyzed to illustrate the proposed algorithms. [ABSTRACT FROM AUTHOR]

Tests for the joint null hypothesis of a unit root based on the components representation of a time series are developed. The proposed testing procedure is designed to detect a unit root as well as guide the practitioner regarding the specification of trend component of a time series. The limiting null distributions of the newly developed F-statistics are derived. Finite sample simulation evidence shows that the F-statistics maintain their size, and have power against the trend-break stationary alternative. The use of our methodology is illustrated through an empirical examination of the US–UK real exchange rate, the UK industrial production, and the UK CPI series. [ABSTRACT FROM AUTHOR]

The problem of testing the population mean vector of high-dimensional multivariate data is considered. Inspired by Roy’s union–intersection test, a generalized high-dimensional likelihood ratio test for the normal population mean vector is proposed. The p -value for the test is obtained by using randomization method, which does not rely on assumptions about the structure of the covariance matrix. An interpretation of the new statistic is given, which does not rely on the normality assumption. Hence the proposed test is also available for non-normal multivariate population. Simulation studies show that the new test offers higher power than other two competing tests when the variables are dependent and performs particularly well for non-normal multivariate population. [ABSTRACT FROM AUTHOR]

A test for ordered categorical variables is of considerable importance, because they are frequently encountered in biomedical studies. This paper introduces a simple ordering test approach for the two-way r × c contingency tables with incomplete counts by developing six test statistics, i.e., the likelihood ratio test statistic, score test statistic, global score test statistic, Hausman–Wald test statistic, Wald test statistic and distance-based test statistic. Bootstrap resampling methods are also presented. The performance of the proposed tests is evaluated with respect to their empirical type I error rates and empirical powers. The results show that the likelihood ratio test statistic based on the bootstrap resampling methods perform satisfactorily for small to large sample sizes. A real example from a wheeze study in six cities is used to illustrate the proposed methodologies. [ABSTRACT FROM AUTHOR]

Large covariance matrices play a fundamental role in various high-dimensional statistics. Investigating the limiting behavior of the eigenvalues can reveal informative structures of large covariance matrices, which is particularly important in high-dimensional principal component analysis and covariance matrix estimation. In this paper, we propose a framework to test the number of distinct population eigenvalues for large covariance matrices, i.e. the order of a Population Spectral Distribution. The limiting distribution of our test statistic for a Population Spectral Distribution of order 2 is developed along with its ( N , p ) consistency, which is clearly demonstrated in our simulation study. We also apply our test to two classical microarray datasets. [ABSTRACT FROM AUTHOR]

The problem of testing the mean vector in a high-dimensional setting is considered. Up to date, most high-dimensional tests for the mean vector only make use of the marginal information from the variables, and do not incorporate the correlation information into the test statistics. A new testing procedure is proposed, which makes use of the covariance information between the variables. The new approach is novel in that it can select important variables that contain evidence against the null hypothesis and reduce the impact of noise accumulation. Simulations and real data analysis demonstrate that the new test has higher power than some competing methods proposed in the literature. [ABSTRACT FROM AUTHOR]

A class of goodness-of-fit tests whose test statistic is an L 2 norm of the difference of the empirical characteristic function of the sample and a parametric estimate of the characteristic function in the null hypothesis, is considered. The null distribution is usually estimated through a parametric bootstrap. Although very easy to implement, the parametric bootstrap can become very computationally expensive as the sample size, the number of parameters or the dimension of the data increase. It is proposed to approximate the null distribution through a weighted bootstrap. The method is studied both theoretically and numerically. It provides a consistent estimator of the null distribution. In the numerical examples carried out, the estimated type I errors are close to the nominal values. The asymptotic properties are similar to those of the parametric bootstrap but, from a computational point of view, it is more efficient. [ABSTRACT FROM AUTHOR]

The class of composite likelihood functions provides a flexible and powerful toolkit to carry out approximate inference for complex statistical models when the full likelihood is either impossible to specify or unfeasible to compute. However, the strength of the composite likelihood approach is dimmed when considering hypothesis testing about a multidimensional parameter because the finite sample behavior of likelihood ratio, Wald, and score-type test statistics is tied to the Godambe information matrix. Consequently, inaccurate estimates of the Godambe information translate in inaccurate p-values. The approach based on a fully nonparametric saddlepoint test statistic derived from the composite score functions is shown to achieve accurate inference. The proposed statistic is asymptotically chi-squared distributed up to a relative error of second order and does not depend on the Godambe information. The validity of the method is demonstrated through simulation studies. [ABSTRACT FROM AUTHOR]

Multiple-testing problems have received much attention. Different strategies have been considered in order to deal with this problem. The false discovery rate (FDR) is, probably, the most studied criterion. On the other hand, the sequential goodness of fit (SGoF), is a recently proposed approach. Most of the developed procedures are based on the independence among the involved tests; however, in spite of being a reasonable proviso in some frameworks, independence is not realistic for a number of practical cases. Therefore, one of the main problems in order to develop appropriate methods is, precisely, the effect of the dependence among the different tests on decisions making. The consequences of the correlation on the z-values distribution in the general multitesting problem are explored. Some different algorithms are provided in order to approximate the distribution of the expected rejection proportions. The performance of the proposed methods is evaluated in a simulation study in which, for comparison purposes, the Benjamini and Hochberg method to control the FDR, the Lehmann and Romano procedure to control the tail probability of the proportion of false positives (TPPFP), and the Beta--Binomial SGoF procedure are considered. Three different dependence structures are considered. As usual, for a better understanding of the problem, several practical cases are also studied. [ABSTRACT FROM AUTHOR]

The Lorenz regression procedure quantifies the inequality of a response explained by a set of covariates. Formally, it gives a weight to each covariate to maximize the concentration index between the response and a weighted average of the covariates. The obtained index is called the explained Gini coefficient. Unlike methods based on decompositions of inequality measures, the procedure does not assume a linear relationship between the response and the covariates. Inference can be performed by noticing a similarity with the monotone rank estimator, introduced in the context of the single-index model. A continuity correction is presented in the presence of discrete covariates. The Lorenz- R 2 is a goodness-of-fit measure evaluating the proportion of explained inequality and is used to build a test of joint significance of several covariates. Monte-Carlo simulations and a real-data example are presented. [ABSTRACT FROM AUTHOR]

• Bayesian hypothesis tests present an alternative to NHST and p-values. • By now, calibration of the power and error rates of Bayesian tests is challenging. • This paper demonstrates how to balance errors and power for nonparametric Bayesian two-sample tests. • The dependence of the prior modelling and influence of sample size is investigated. • Bayesian nonparametric two-sample tests can be calibrated via the presented results. Hypothesis testing is a central statistical method in the biomedical sciences. The ongoing debate about the concept of statistical significance and the reliability of null hypothesis significance tests (NHST) and p-values has brought the advent of various Bayesian hypothesis tests as possible alternatives, which often employ the Bayes factor. However, careful calibration of the prior parameters is necessary for the type I error rates or power of these alternatives to be any better. Also, the availability of various Bayesian tests for the same statistical problem leads to the question which test to choose based on which criteria. Recently proposed Bayesian nonparametric two-sample tests are analyzed with regard to their type I error rates and power to detect an effect. Results show that approaches vary substantially in their ability to control the type I and II errors, and it is shown how to select the prior parameters to balance power and type I error control. This allows for prior elicitation and power analyses based on objective criteria like type I and II error rates even when conducting a Bayesian nonparametric two-sample test. Also, it is shown that existing nonparametric Bayesian two-sample tests are adequate only to test for location-shifts. Together, the results provide guidance how to perform a nonparametric Bayesian two-sample test while simultaneously improving the reliability of research. [ABSTRACT FROM AUTHOR]

Abstract: A selection procedure with no optimization step called LOLA, for Learning Out of Leaders with Adaptation is proposed. LOLA is an auto-driven algorithm with two thresholding steps. The consistency of the LOL procedure (the non adaptive version of LOLA) is proved under sparsity conditions and simulations are conducted to illustrate the practical good performances of LOLA. The behavior of the algorithm is studied when instrumental variables are artificially added without a priori significant connection to the model. Finally, the problem of empirically verifying the conditional convergence hypothesis used in economics concerning the growth rate is studied. To avoid unnecessary discussion about the choice and the pertinence of instrumental variables, the model is embedded in a very high dimensional setting. Using the LOLA algorithm, a solution for modeling the link between the growth rate and the initial level of the gross domestic product is provided and the convergence hypothesis is empirically proved. [Copyright &y& Elsevier]

Abstract: A new method is proposed for testing multiple hypotheses with equality and inequality constraints on the parameters of interest. The method is based on the fractional Bayes factor with a modification that the updated prior is centered on the boundary of the constrained parameter space under investigation. The resulting prior adjusted default Bayes factors work as an “Ockham’s razor” when testing inequality constrained hypotheses, which is not the case for the fractional Bayes factor. Two different types of prior adjusted default Bayes factors are considered. In the first type, the updated prior is based on imaginary training data. Analytical and numerical examples show that this criterion converges fastest to a true inequality constrained hypothesis. In the second type, the updated prior is based on empirical training data. This second criterion only outperforms the fractional Bayes factor in the case of small samples. [Copyright &y& Elsevier]

Abstract: A recently proposed Bayesian model selection technique, stochastic model specification search, is carried out to discriminate between two trend generation hypotheses. The first is the trend-stationary hypothesis, for which the trend is a deterministic function of time and the short run dynamics are represented by a stationary autoregressive process. The second is the difference-stationary hypothesis, according to which the trend results from the cumulation of the effects of random disturbances. A difference-stationary process may originate in two ways: from an unobserved components process adding up an integrated trend and an orthogonal transitory component, or implicitly from an autoregressive process with roots on the unit circle. The different trend generation hypotheses are nested within an encompassing linear state space model. After a reparameterisation in non-centred form, the empirical evidence supporting a particular hypothesis is obtained by performing variable selection on the model components, using a suitably designed Gibbs sampling scheme. The methodology is illustrated with reference to a set of US macroeconomic time series which includes the traditional Nelson and Plosser dataset. The conclusion is that most series are better represented by autoregressive models with time-invariant intercept and slope and coefficients that are close to boundary of the stationarity region. The posterior distribution of the autoregressive parameters provides useful insight on quasi-integrated nature of the specifications selected. [Copyright &y& Elsevier]

Abstract: The NDARMA model is a discrete counterpart to the usual ARMA model, which can be applied to purely categorical processes. NDARMA processes are shown to be -mixing, so it is possible to find asymptotic expressions for the distribution of several types of statistics. Such asymptotic properties are useful for hypothesis testing or other inferential procedures. This is exemplified by considering the Gini index and the entropy as measures of marginal dispersion, the Pearson statistic for checking the goodness-of-fit with regard to a hypothetical marginal distribution, and several measures of signed or unsigned serial dependence. For each of these cases, the obtained asymptotic approximations are also compared to the empirically observed behavior in time series of finite length. Practical applications are illustrated by a real-data example. [Copyright &y& Elsevier]

Abstract: In longitudinal cluster randomized clinical trials (cluster-RCT), subjects are nested within a higher level unit such as clinics and are evaluated for outcome repeatedly over the study period. This study design results in a three level hierarchical data structure. When the primary goal is to test the hypothesis that an intervention has an effect on the rate of change in the outcome over time and the between-subject variation in slopes is substantial, the subject-specific slopes are often modeled as random coefficients in a mixed-effects linear model. In this paper, we propose approaches for determining the samples size for each level of a 3-level hierarchical trial design based on ordinary least squares (OLS) estimates for detecting a difference in mean slopes between two intervention groups when the slopes are modeled as random. Notably, the sample size is not a function of the variances of either the second or the third level random intercepts and depends on the number of second and third level data units only through their product. Simulation results indicate that the OLS-based power and sample sizes are virtually identical to the empirical maximum likelihood based estimates even with varying cluster sizes. Sample sizes for random versus fixed slope models are also compared. The effects of the variance of the random slope on the sample size determinations are shown to be enormous. Therefore, when between-subject variations in outcome trends are anticipated to be significant, sample size determinations based on a fixed slope model can result in a seriously underpowered study. [Copyright &y& Elsevier]

Abstract: We consider the problem of testing for perfect rankings in ranked set sampling (RSS). By using a new algorithm for computing the probability that specified independent random variables have a particular ordering, we find most powerful rank tests of the null hypothesis of perfect rankings against fully specified alternatives. We compare the power of these most powerful rank tests to that of existing rank tests in the literature, and we find that the existing tests are surprisingly close to optimal over a wide range of alternatives to perfect rankings. This finding holds both for balanced RSS and for unbalanced RSS cases where the different ranks are not equally represented in the sample. We find that the best of the existing tests is the test that rejects when the null probability of the observed ranks is small, and we provide a new, more efficient R function for computing the test statistic. [Copyright &y& Elsevier]

Abstract: This paper discusses nonparametric comparison of survival functions when one observes only interval-censored failure time data (Peto and Peto, 1972; Sun, 2006; Zhao et al., 2008). For the problem, a few procedures have been proposed in the literature. However, most of the existing test procedures determine the test results or -values based on ad hoc methods or the permutation approach. Furthermore for the test procedures whose asymptotic distributions have been derived, the results are only for the null hypothesis. In other words, no nonparametric test procedure exists that has a known asymptotic distribution under the alternative hypothesis and thus can be employed to carry out the power and test size calculation. In this paper, a new class of generalized log-rank tests is proposed and their asymptotic distributions are derived under both null and alternative hypotheses. A simulation study is conducted to assess their performance for finite sample situations and an illustrative example is provided. [Copyright &y& Elsevier]

Abstract: A new test of hypothesis for classifying stationary time series based on the bias-adjusted estimators of the fitted autoregressive model is proposed. It is shown theoretically that the proposed test has desirable properties. Simulation results show that when time series are short, the size and power estimates of the proposed test are reasonably good, and thus this test is reliable in discriminating between short-length time series. As the length of the time series increases, the performance of the proposed test improves, but the benefit of bias-adjustment reduces. The proposed hypothesis test is applied to two real data sets: the annual real GDP per capita of six European countries, and quarterly real GDP per capita of five European countries. The application results demonstrate that the proposed test displays reasonably good performance in classifying relatively short time series. [Copyright &y& Elsevier]

Abstract: Storey’s method for multiple hypothesis testing “the Optimal Discovery Procedure” (ODP) minimising the false discovery rate (FDR) and giving p-values and q-values (estimates of FDR) for each test, was extended by iteration to enforce consistency between the p-values of the tests and the binary parameters defining which data points contribute to the fitted null hypothesis. These parameters arise when the null hypothesis has to be estimated from the data. The ODP as previously described, is only optimal for fixed values of these parameters. The extension proposed here requires the introduction of a cut-off parameter for the p-values. Motivated by using this method to analyse a set of pairs of frequencies representing gene expression for a set of genes in two libraries, from which it was desired to select those that are most likely to be not following the null hypothesis that the frequency ratio is a fixed unknown number, this method was tested by analysing many similar simulated datasets. The results showed that the ODP modified by iteration could be improved sometimes greatly by a suitable choice of the cut-off parameter, but varying this parameter alone may not lead to the globally optimal solution because statistical testing based on the binomial distribution is more efficient than using a form of the ODP when the number of non-null hypotheses in the data is small, but the reverse is true when it is large. This may be an effect of using discrete data. Efficiency here is defined in terms of the expected proportion of errors that occur (q-value) when a given proportion of the data is declared “significant” (i.e. the null hypothesis is believed not to hold for them). An improved version of the ODP along these lines is likely to have numerous applications such as in the optimised search for candidate genes that show unusual expression patterns for example when more than two experimental conditions are simultaneously compared and to cases when additional categorical variables or a time series is present in the experimental design. [Copyright &y& Elsevier]

Abstract: We study the problem of fitting ellipses to observed points in the context of Errors-In-Variables regression analysis. The accuracy of fitting methods is characterized by their variances and biases. The variance has a theoretical lower bound (the KCR bound), and many practical fits attend it, so they are optimal in this sense. There is no lower bound on the bias, though, and in fact our higher order error analysis (developed just recently) shows that it can be eliminated, to the leading order. Kanatani and Rangarajan recently constructed an algebraic ellipse fit that has no bias, but its variance exceeds the KCR bound; so their method is optimal only relative to the bias. We present here a novel ellipse fit that enjoys both optimal features: the theoretically minimal variance and zero bias (both to the leading order). Our numerical tests confirm the superiority of the proposed fit over the existing fits. [Copyright &y& Elsevier]

Abstract: We study the problems of hypothesis testing and point estimation for the correlation coefficient between the disturbances in the system of two seemingly unrelated regression equations. An objective Bayesian solution to each problem is proposed based on combined use of the invariant loss function and the objective prior distribution for the unknown model parameters. It is shown that this new solution possesses an invariance property under monotonic reparameterization of the quantity of interest. The performance of the proposed solution is examined through a simulation study. Furthermore, the solution is illustrated by an application to the real annual data for analyzing the investment model. [Copyright &y& Elsevier]

Abstract: The paper addresses a common problem in the analysis of high-dimensional high-throughput “omics” data, which is parameter estimation across multiple variables in a set of data where the number of variables is much larger than the sample size. Among the problems posed by this type of data are that variable-specific estimators of variances are not reliable and variable-wise tests statistics have low power, both due to a lack of degrees of freedom. In addition, it has been observed in this type of data that the variance increases as a function of the mean. We introduce a non-parametric adaptive regularization procedure that is innovative in that (i) it employs a novel “similarity statistic”-based clustering technique to generate local-pooled or regularized shrinkage estimators of population parameters, (ii) the regularization is done jointly on population moments, benefiting from C. Stein’s result on inadmissibility, which implies that usual sample variance estimator is improved by a shrinkage estimator using information contained in the sample mean. From these joint regularized shrinkage estimators, we derived regularized t-like statistics and show in simulation studies that they offer more statistical power in hypothesis testing than their standard sample counterparts, or regular common value-shrinkage estimators, or when the information contained in the sample mean is simply ignored. Finally, we show that these estimators feature interesting properties of variance stabilization and normalization that can be used for preprocessing high-dimensional multivariate data. The method is available as an R package, called ‘MVR’ (‘Mean–Variance Regularization’), downloadable from the CRAN website. [Copyright &y& Elsevier]

Abstract: A natural methodology for discriminating functional data is based on the distances from the observation or its derivatives to group representative functions (usually the mean) or their derivatives. It is proposed to use a combination of these distances for supervised classification. Simulation studies show that this procedure performs very well, resulting in smaller testing classification errors. Applications to real data show that this technique behaves as well as–and in some cases better than–existing supervised classification methods for functions. [Copyright &y& Elsevier]

Abstract: This paper tests the null hypothesis of stationarity against the alternative of changes in persistence for sequences in the domain of attraction of a stable law. The proposed moving ratio test is valid for multiple changes in persistence while the previous residual based ratio tests are designed for processes displaying only a single change. We show that the new test is consistent whether the process changes from to or vice versa. And it is easy to identify the direction of detected change points. In particular, a bootstrap approximation method is proposed to determine the critical values for the null distribution of the test statistic containing unknown tail index. We also propose a two step approach to estimate the change points. Numerical evidence suggests that our test performs well in finite samples. In addition, we show that our test is still powerful for changes between short and long memory, and displays no tendency to spuriously over-reject null in favor of a persistence change if the process is actually throughout. Finally, we illustrate our test using the US inflation rate data and a set of high frequency stock closing price data. [Copyright &y& Elsevier]

Abstract: In this article, we introduce a new method of image pixel classification. Our method is a nonparametric classification method which uses combined evidence from the multiple hypothesis testings and minimum distance to carry out the classification. Our work is motivated by the test-based classification introduced by . We focus on binary and multiclass classification of image pixels taking into account both equal and unequal prior probability of classes. Experiments show that our method works better in classifying image pixels in comparison with some of the standard classification methods such as linear discriminant analysis, quadratic discriminant analysis, classification tree, the polyclass method, and the Liao and Akritas method. We apply our classifier to perform image segmentation. Experiments show that our test-based segmentation has excellent edge detection and texture preservation property for both gray scale and color images. [Copyright &y& Elsevier]

Abstract: For the purpose of comparison between several independent populations, many procedures exist for testing equality of means or medians among the groups. However, the mean or the median do not determine the entire distribution. This paper addresses the problem of testing the equality of quantiles of several normal distributions. We propose an approximate test based on large sample method and an exact procedure based on a generalized -value. An extensive simulation study was conducted to evaluate the size and powers of these two tests. Simulation results show that the generalized -value approach performs very satisfactorily even for small samples while the approximate method exhibits poor Type I error control. A robustness study was done for power-exponential distribution and -distribution. Finally, the proposed methods are applied to two real examples. [Copyright &y& Elsevier]

Abstract: Statistical procedures for the equality of two and univariate distributions based on samples of dependent observations are proposed in this work. The test statistics are distances of standard empirical and characteristic function processes. The -values of the tests are obtained from a version of the multiplier central limit theorem whose asymptotic validity is established. Simple formulas for the test statistics and their multiplier versions in terms of multiplication of matrices are provided. Simulations under many patterns of dependence characterized by copulas show the good behavior of the tests in small samples, both in terms of their power and of their ability to keep their nominal level under the null hypothesis. [Copyright &y& Elsevier]

Abstract: Multiple testing analysis and clustering methodologies are usually applied in microarray data analysis. A combination of both methods to deal with multiple comparisons among groups obtained from microarray expressions of genes is proposed. Assuming normal data, a statistic which depends on sample means and sample variances, distributed as a non-central -distribution is defined. As multiple comparisons among groups are considered, a mixture of non-central -distributions is derived. The estimation of the components of mixtures is obtained via a Bayesian approach, and the model is applied in a multiple comparison problem from a microarray experiment obtained from gorilla, bonobo and human cultured fibroblasts. [Copyright &y& Elsevier]

Abstract: The construction of a multivariate two sample test is considered. An attractive approach to this problem, for instance when the data contain missing values or the number of variables is large, is to form an overall test by combining the componentwise test statistics. This can be done via their -values or some other transformation. An important problem is how to perform the combination, as the relative power of a given combination will depend on the unknown true alternative. Recently, an approach has been proposed that makes use of the data to identify an appropriate combination. The method forms a pool of potential combinations of the componentwise -values, setting the overall test statistic to the minimum -value across the pool. One drawback of the approach, however, is that it does not utilize dependence between the componentwise tests, and thus potentially ignores valuable information. This issue is addressed, and two approaches are described that make use of the data to (1) determine which tests to combine; and (2) how best to utilize the between test statistic dependence. Simulations show that the proposed methods can lead to a substantial increase in power. An application to a dietary intervention study is given. [Copyright &y& Elsevier]

Abstract: This paper uses Bayesian tree models for statistical benchmarking in data sets with awkward marginals and complicated dependence structures. The method is applied to a very large database on corporate performance over the last four decades. The results of this study provide a formal basis for making cross-peer-group comparisons among companies in very different industries and operating environments. This is done by using models for Bayesian multiple hypothesis testing to determine which firms, if any, have systematically out-performed their peer groups over time. We conclude that systematic out-performance, while it seems to exist, is quite rare worldwide. [Copyright &y& Elsevier]

Abstract: Testing non-inferiority in active-controlled clinical trials examines whether a new procedure is, to a pre-specified amount, no worse than an existing procedure. To assess non-inferiority between two procedures using clustered matched-pair binary data, two new statistical tests are systematically compared to existing tests. The calculation of corresponding confidence interval is also proposed. None of the tests considered requires structural within-cluster correlation or distributional assumptions. The results of an extensive Monte Carlo simulation study illustrate that the performance of the statistics depends on several factors including the number of clusters, cluster size, probability of success in the test procedure, the homogeneity of the probability of success across clusters, and the intra-cluster correlation coefficient (ICC). In evaluating non-inferiority for a clustered matched-pair study, one should consider all of these issues when choosing an appropriate test statistic. The ICC-adjusted test statistic is generally recommended to effectively control the nominal level when there is constant or small variability of cluster sizes. For a greater number of clusters, the other test statistics maintain the nominal level reasonably well and have higher power. Therefore, with the carefully designed clustered matched-pair study, a combination of the statistics investigated may serve best in data analysis. Finally, to illustrate the practical application of the recommendations, a real clustered matched-pair collection of data is used to illustrate testing non-inferiority. [Copyright &y& Elsevier]

Abstract: The positive and negative predictive values of a binary diagnostic test are measures of the clinical accuracy of the diagnostic test, which depend on the sensitivity and specificity of the diagnostic test and the disease prevalence, and therefore they are two interdependent parameters. The comparisons of predictive values in paired designs do not consider the dependence between predictive values. A global hypothesis test has been studied in order to simultaneously compare the predictive values of two or more binary diagnostic tests when the binary tests and the gold standard are applied to all of the individuals in a random sample. This global hypothesis test is an asymptotic hypothesis test based on the chi-square distribution. Simulation experiments have been carried out in order to study the type I error and the power of the global hypothesis test when comparing the predictive values of two and three binary diagnostic tests, respectively. From the results of the simulation experiments, a method has been proposed to simultaneously compare the predictive values of two or more binary diagnostic tests. The results have been applied to the diagnosis of coronary disease. [Copyright &y& Elsevier]

Abstract: In image processing, image similarity indices evaluate how much structural information is maintained by a processed image in relation to a reference image. Commonly used measures, such as the mean squared error (MSE) and peak signal to noise ratio (PSNR), ignore the spatial information (e.g. redundancy) contained in natural images, which can lead to an inconsistent similarity evaluation from the human visual perception. Recently, a structural similarity measure (SSIM), that quantifies image fidelity through estimation of local correlations scaled by local brightness and contrast comparisons, was introduced by . This correlation-based SSIM outperforms MSE in the similarity assessment of natural images. However, as correlation only measures linear dependence, distortions from multiple sources or nonlinear image processing such as nonlinear filtering can cause SSIM to under- or overestimate the true structural similarity. In this article, we propose a new similarity measure that replaces the correlation and contrast comparisons of SSIM by a term obtained from a nonparametric test that has superior power to capture general dependence, including linear and nonlinear dependence in the conditional mean regression function as a special case. The new similarity measure applied to images from noise contamination, filtering, and watermarking, provides a more consistent image structural fidelity measure than commonly used measures. [Copyright &y& Elsevier]

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: 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: 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: 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: 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: 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: 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: 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: 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]