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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]

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 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: 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: 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]

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: 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: 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: 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: 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]