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Canonical correlation analysis (CCA) is a popular statistical tool in multivariate analysis. A regularized version is often used to stabilize the estimate. Motivated by recent interests in sketching estimates for linear regression problems which try to address the computational problem associated with massive data sets, here we investigate the sketched estimation for CCA, which includes the random subsampling approach as a special case. Some theoretical results are established based on perturbation theory. The method is also illustrated via some Monte Carlo studies and a real data analysis. [ABSTRACT FROM AUTHOR]

The classical theory of reinforcement learning focused on the tabular setting when states and actions are finite, or for linear representation of the value function in a finite-dimensional approximation. Establishing theory on general continuous state and action space requires a careful treatment of complexity theory of appropriately chosen function spaces and the iterative update of the value function when stochastic gradient descent (SGD) is used. For the classical prediction problem in reinforcement learning based on i.i.d. streaming data in the framework of reproducing kernel Hilbert spaces, we establish polynomial sample complexity taking into account the smoothness of the value function. In particular, we prove that the gradient descent algorithm efficiently computes the value function with appropriately chosen step sizes, with a convergence rate that can be close to 1 / N , which is the best possible rate for parametric SGD. The advantages of using the gradient descent algorithm include its computational convenience and it can naturally deal with streaming data. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of comparing the population means of two groups of independent observations. An approximate randomization test procedure based on the test statistic of Chen & Qin (2010) is proposed. The asymptotic behaviour of the test statistic, as well as the randomized statistic, is studied under weak conditions. In our theoretical framework, observations are not assumed to be identically distributed even within groups. No condition on the eigenstructure of the covariance matrices is imposed. Furthermore, the sample sizes of the two groups are allowed to be unbalanced. Under general conditions, all possible asymptotic distributions of the test statistic are obtained. We derive the asymptotic level and local power of the approximate randomization test procedure. Our theoretical results show that the proposed test procedure can adapt to all possible asymptotic distributions of the test statistic, always has the correct test level asymptotically and has good power behaviour. Our numerical experiments show that the proposed test procedure has favourable performance compared with several alternative test procedures. [ABSTRACT FROM AUTHOR]

There has been a growing interest in solving consensus optimization problems in a multi-agent system. It is known that there is an exactness-speed dilemma for decentralized optimization for the naive gradient method, where either we have fast linear convergence to a neighborhood of size O (η) using a fixed constant step size η , or slow convergence to the exact optimizer with a decreasing step size. We reinvestigate a special case of this problem from a statistical point of view, where each agent's local function is a sample estimate of a common population function. It is shown that when considering the convergence to the population target instead of to the exact consensual solution, the convergence is linear up to the statistical accuracy of the problem, using a step size only depending on the network characteristics instead of the sample size N. The objective function is not required to be strongly convex (but their statistical limit is), which allows for example the absolute deviation function which is used in median regression. Such results are in stark contrast to the optimization literature, where strong convexity of the objective function is necessary for linear convergence. [ABSTRACT FROM AUTHOR]

Quantile regression with a total variation penalty was previously proposed due to its computational expediency as well as its local adaptiveness. However, the convergence rate of the method in this setting has been not rigorously established. In this short communication, we establish the convergence rate of Op(n−1/3) for the penalized estimator which is the same as in penalized least squares regression. Different from penalized least squares regression, in order to deal with the quantile loss function, we heavily rely on the Rademacher complexity of the class of functions of bounded variation. [ABSTRACT FROM AUTHOR]

In this article, we propose a new method for estimating the number of equal components m0 of two m-dimensional population means when m is large. The proposed method can be used to estimate the number of equally expressed or differentially expressed genes in DNA microarray studies. It can also be applied in the step of estimating m0 in adaptive false discovery rate controlling procedures. Simulation results show that the bias of the moment estimator is very small for both normal and non normal data. It has higher precision than existing methods in most cases. It has more evident advantage under non normal data. [ABSTRACT FROM AUTHOR]

This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. The distortion functions for this kind of measurement errors are modelled under a general identifiability condition. For parameter estimation, we propose two calibration procedures: the conditional mean calibration based least squares estimation and the varying coefficient based estimation. The asymptotic normal confidence intervals and empirical likelihood confidence intervals are also proposed. Simulation studies are conducted to compare the proposed calibration procedures and a real example is analysed to illustrate its practical usage. [ABSTRACT FROM AUTHOR]

Multiple permutation testing is a test method combining the idea of permutation and multiple testing. It first employs the permutation testing to calculate p-values for single tests, and then determines the result based on criteria of multiple testing. To well control type I error rate, the classical method needs a large number of permutation samples for calculating p-values. When the dimension of data, m, is high, the permutation procedure is very time consuming. This paper proposes a components-combined algorithm for the type I error rate control. The new algorithm only requires a small and fixed number of permutation samples for any dimension of data and can achieve the same approximation accuracy of p-values as the classical method. Therefore, it reduces the computational amount of multiple permutation testing procedures from to . The algorithm is then applied to several testing problems and the power performance is examined by simulations and comparisons with existing methods. [ABSTRACT FROM AUTHOR]

Testing for independence between two random vectors is a fundamental problem in statistics. When the dimension of these two random vectors are fixed, the existing tests based on the distance covariance and Hilbert–Schmidt independence criterion with many desirable properties, including the capacity to capture linear and non-linear dependence. However, these tests may fail to capture the non-linear dependence due to the "curse of dimensionality" when the random vectors are high dimensional. To attack this problem, we propose a general framework for testing the dependence of two random vectors to randomly select two subspaces consisting of components of the vectors, respectively. To enhance the performance of this method, we repeatedly implement this procedure to construct the final test statistic. The new method can also work for non-linear dependence detection in a high-dimensional setup. Theoretically, if the replication time tends to infinity to get the final statistic, we can avoid potential power loss caused by lousy subspaces. Therefore, the two proposed tests are consistent with general alternatives. The weak limit under the null hypothesis is normal; thus, determining critical value need not resort to resampling approximation. We demonstrate the finite-sample performance of the proposed test by using Monte Carlo simulations and the analysis for a real-data example. [ABSTRACT FROM AUTHOR]

Background: Suboptimal health status (SHS) is the third state between good health and disease. SHS is the clinical or pre-disease status of psychosomatic disease and a major global public health challenge. Although its underlying causes remain unclear, lifestyle is one of the most important factors affecting health status. Methods: A cross-sectional survey was conducted at Renmin University of China in September of 2015. Data were collected from college freshmen using a questionnaire covering characteristics, lifestyle, nutrition status, and health status. A total of 6025 questionnaires were distributed during the study period, and 5344 completed responses were received. Results: The prevalence rates for the "healthy," "SHS," and "disease" groups of college freshmen were 46.7% (2433), 51.2% (2667), and 2.1% (111), respectively. It is notable that health status was significantly positively correlated with lifestyle (Spearman's r = 0.4435, p <0.001). The multivariate Logistic regression results showed that students who were relatively younger and students from rural areas had a higher percentage of SHS. Good sleep quality (aOR = 0.650, 95%CI = 0.612-0.690), abundant physical exercise (aOR = 0.889, 95%CI = 0. 845-0.933), and adequate nutrition intake (aOR = 0.868, 95%CI = 0.864-0.908) are negatively associated with SHS. Overuse of electronic devices (aOR= 1.066, 95%CI = 1.013-1.121), smoking (aOR= 1.824, 95%CI = 1.195-2. 755), and weight loss (aOR= 1.255, 95%CI = 1.043-1.509) are positively associated with SHS. Conclusions: Poor lifestyle behaviors are associated with SHS. In particular, the overuse of electronic devices is one of underlying causes of SHS. By altering lifestyle behaviors for the better, the health statuses of these college freshmen can be effectively improved. [ABSTRACT FROM AUTHOR]

The Hosmer–Lemeshow test is a widely used method for evaluating the goodness of fit of logistic regression models. But its power is much influenced by the sample size, like other chi-square tests. Paul, Pennell, and Lemeshow (2013) considered using a large number of groups for large data sets to standardize the power. But simulations show that their method performs poorly for some models. In addition, it does not work when the sample size is larger than 25,000. In the present paper, we propose a modified Hosmer–Lemeshow test that is based on estimation and standardization of the distribution parameter of the Hosmer–Lemeshow statistic. We provide a mathematical derivation for obtaining the critical value and power of our test. Through simulations, we can see that our method satisfactorily standardizes the power of the Hosmer–Lemeshow test. It is especially recommendable for enough large data sets, as the power is rather stable. A bank marketing data set is also analyzed for comparison with existing methods. [ABSTRACT FROM AUTHOR]

Generalized Additive Partial Linear Models (GAPLMs) are appealing for model interpretation and prediction. However, for GAPLMs, the covariates and the degree of smoothing in the nonparametric parts are often difficult to determine in practice. To address this model selection uncertainty issue, we develop a computationally feasible Model Averaging (MA) procedure. The model weights are data-driven and selected based on multifold Cross-Validation (CV) (instead of leave-one-out) for computational saving. When all the candidate models are misspecified, we show that the proposed MA estimator for GAPLMs is asymptotically optimal in the sense of achieving the lowest possible Kullback-Leibler loss. In the other scenario where the candidate model set contains at least one quasi-correct model, the weights chosen by the multifold CV are asymptotically concentrated on the quasi-correct models. As a by-product, we propose a variable importance measure to quantify the importances of the predictors in GAPLMs based on the MA weights. It is shown to be able to asymptotically identify the variables in the true model. Moreover, when the number of candidate models is very large, a model screening method is provided. Numerical experiments show the superiority of the proposed MA method over some existing model averaging and selection methods. for this article are available online. [ABSTRACT FROM AUTHOR]

The Birnbaum-Saunders distribution is widely used in fields such as survival analysis. In this paper, we use a new method to construct confidence intervals for the shape parameter of the Birnbaum-Saunders distribution and find it superior to some existing methods. Our method can be called the 'joint pivot method' as we obtain the confidence interval by uniting two pivots. Furthermore, we find that the joint pivot method can also be used to solve the Behrens-Fisher problem. Simulation studies show that the joint pivot method is comparable with some commonly practiced ones. Finally, we analyse two real data sets to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]

Negative binomial group distribution was proposed in the literature which was motivated by inverse sampling when considering group inspection: products are inspected group by group, and the number of non-conforming items of a group is recorded only until the inspection of the whole group is finished. The non-conforming probabilitypof the population is thus the parameter of interest. In this paper, the confidence interval construction for this parameter is investigated. The common normal approximation and exact method are applied. To overcome the drawbacks of these commonly used methods, a composite method that is based on the confidence intervals of the negative binomial distribution is proposed, which benefits from the relationship between negative binomial distribution and negative binomial group distribution. Simulation studies are carried out to examine the performances of our methods. A real data example is also presented to illustrate the application of our method. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate the goodness-of-fit test of partial linear regression models when the true variable in the linear part is not observable but the surrogate variable $$\tilde{X}$$ , the variable in the non-linear part $$T$$ and the response $$Y$$ are exactly measured. In addition, an independent validation data set for $$X$$ is available. By a transformation, it is found that we only need to check whether the linear model is plausible or not. We estimate the conditional expectation of $$X$$ under a given the surrogate variable with the help of the validation sample. Finally, a residual-based empirical test for the partial linear models is constructed. A nonparametric Monte Carlo test procedure is used, and the null distribution can be well approximated even when data are from alternative models converging to the hypothetical model. Simulation results show that the proposed method works well. [ABSTRACT FROM AUTHOR]

We are concerned with massive data which are possibly heterogeneous and scattered at different locations. We introduce a communication-efficient distributed algorithm to estimate the rank-deficient loading matrix in reduced rank regressions. The distributed algorithm, which proceeds iteratively, reduces the computational complexity substantially. During each iteration, it yields a closed-form solution and refines the previous estimators gradually. After a finite number of iterations, the final solution estimates the rank consistently, and more importantly, achieves the oracle rate. We recast sufficient dimension reduction methods under the framework of reduced rank regressions, which enables us to recover the central subspace and simultaneously estimate its structural dimension. We demonstrate the efficiency of our proposed distributed algorithm through simulations and an application to the airline on-line performance dataset consisting of 118,914,458 observations. [ABSTRACT FROM AUTHOR]

This paper aims at investigating model checking for parametric models with response missing at random which is a more general missing mechanism than missing completely at random. Different from existing approaches, two tests have normal distributions as the limiting null distributions no matter whether the inverse probability weight is estimated parametrically or nonparametrically. Thus, $$p$$ values can be easily determined. This observation shows that slow convergence rate of nonparametric estimation does not have significant effect on the asymptotic behaviors of the tests although it may have impact in finite sample scenarios. The tests can detect the alternatives distinct from the null hypothesis at a nonparametric rate which is an optimal rate for locally smoothing-based methods in this area. Simulation study is carried out to examine the performance of the tests. The tests are also applied to analyze a data set on monozygotic twins for illustration. [ABSTRACT FROM AUTHOR]

In this paper, from the estimating equation-based sufficient dimension reduction method in the literature, its robust version is proposed to alleviate the impact from outliers. To achieve this, a robust nonparametric regression estimator is suggested. The estimator is plugged in the estimating equation of the semiparametric sufficient dimension reduction to obtain robust estimator for the central subspace. The asymptotic properties and robustness of the estimator are investigated. Numerical simulation and real data analysis are conducted to examine the performance of the estimators. [ABSTRACT FROM AUTHOR]

In parameter estimation, it is not a good choice to select a 'best model' by some criterion when there is model uncertainty. Model averaging is commonly used under this circumstance. In this paper, transformation-based model averaged tail area is proposed to construct confidence interval, which is an extension of model averaged tail area method in the literature. The transformation-based model averaged tail area method can be used for general parametric models and even non-parametric models. Also, it asymptotically has a simple formula when a certain transformation function is applied. Simulation studies are carried out to examine the performance of our method and compare with existing methods. A real data set is also analyzed to illustrate the methods. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers estimation of the semiparametric multi-index model with missing covariates at random. A weighted estimating equation is suggested by invoking the inverse selection probability approach, and estimators of the indices are respectively defined when the selection probability is known in advance, is estimated parametrically and nonparametrically. The consistency is provided. For the single-index model, the large sample properties show that the estimators with both parametric and nonparametric plug-in estimations can play an important role to achieve smaller limiting variances than the estimator with the true selection probability. Simulation studies are carried out to assess the finite sample performance of the proposed estimators. The proposed methods are applied to an AIDS clinical trials dataset to examine which method could be more efficient. A horse colic dataset is also analyzed for illustration. [Copyright &y& Elsevier]

In this paper, we consider the goodness-of-fit for checking whether the nonparametric function in a partial linear regression model with missing covariate at random is a parametric one or not. We estimate the selection probability by using parametric and nonparametric approaches. Two score type tests are constructed with the estimated selection probability. The asymptotic distributions of the test statistics are investigated under the null and local alterative hypothesis. Simulation studies are carried out to examine the finite sample performance of the sizes and powers of the tests. We apply the proposed procedure to a data set on the AIDS clinical trial group (ACTG 315) study. [ABSTRACT FROM AUTHOR]

In this paper, we propose a test on the parametric form of the coefficient functions in the varying coefficient model with missing response. Two groups of completed data sets are constructed by using imputation and inverse probability weighting methods respectively. By noting that the coefficient part can be a regression function for a specific model, we construct two empirical process-based tests. The asymptotical distributions of the proposed tests under null and local alternative hypothesis are investigated respectively. Simulation study is carried out to show the power performance of the test. We illustrate the proposed approaches with an environmental data set. [ABSTRACT FROM AUTHOR]

In this paper, we investigate checking the adequacy of varying coefficient models with response missing at random. In doing so, we first construct two completed data sets based on imputation and marginal inverse probability weighted methods, respectively. The empirical process-based tests by using these two completed data sets are suggested and the asymptotic properties of the test statistics under the null and local alternative hypotheses are studied. Because the limiting null distribution is intractable, a Monte Carlo approach is applied to approximate the distribution to determine critical values. Simulation studies are carried out to examine the performance of our method, and a real data set from an environmental study is analyzed for illustration. [ABSTRACT FROM AUTHOR]

Two-stage design is a well-known cost-effective way for conducting biomedical studies when the exposure variable is expensive or difficult to measure. Recent research development further allowed one or both stages of the two-stage design to be outcome dependent on a continuous outcome variable. This outcome-dependent sampling feature enables further efficiency gain in parameter estimation and overall cost reduction of the study (e.g. Wang, X. and Zhou, H., 2010. Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling. Biometrics 66, 502–511; Zhou, H., Song, R., Wu, Y. and Qin, J., 2011. Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome. Biometrics 67, 194–202). In this paper, we develop a semiparametric mixed effect regression model for data from a two-stage design where the second-stage data are sampled with an outcome-auxiliary-dependent sample (OADS) scheme. Our method allows the cluster- or center-effects of the study subjects to be accounted for. We propose an estimated likelihood function to estimate the regression parameters. Simulation study indicates that greater study efficiency gains can be achieved under the proposed two-stage OADS design with center-effects when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a dataset from the Collaborative Perinatal Project. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a model checking problem for general linear models with randomly missing covariates. Two types of score type tests with inverse probability weight, which is estimated by parameter and nonparameter methods respectively, are proposed to this goodness of fit problem. The asymptotic properties of the test statistics are developed under the null and local alternative hypothesis. Simulation study is carried out to present the performance of the sizes and powers of the tests. We illustrate the proposed method with a data set on monozygotic twins. [Copyright &y& Elsevier]

In this study, we consider the testing problem about the null hypothesis that the nonlinear part in the partial linear regression model with missing response at random is a parametric function or not against the alternative that it is nonparametric. By imputation and inverse probability weighting methods, we then construct two completed data sets. Two empirical process-based tests, from these completed data sets, are introduced. Under the null hypothesis and local alterative hypotheses, the limiting null distributions and power study of the test statistics are, respectively, investigated. A nonparametric Monte Carlo test procedure, which can automatically make the test procedure scale-invariant even when the test statistics are not scale-invariant, is applied to approximate the limiting null distributions of the test statistics. Simulation study is carried out to examine the performance of the tests. We illustrate the proposed method with a real data set on monozygotic twins. [ABSTRACT FROM PUBLISHER]

In this article, we develop a method for checking the estimation equations, which is for joint estimation of the regression parameters and the overdispersion parameters, based on one dimension projected covariate. This method is different from the general testing methods in that our proposed method can be applied to high-dimensional response while the classical testing methods can not be extended to high dimension problem simply to construct a powerful test. Furthermore, the properties of the test statistics are investigated and Nonparametric Monte Carlo Test (NMCT) is suggested to determine the critical values of the test statistics under null hypothesis. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider subset deletion diagnostics for fixed effects (coefficient functions), random effects and one variance component in varying coefficient mixed models (VCMMs). Some simple updated formulas are obtained, and based on which, Cook’s distance, joint influence and conditional influence are also investigated. Besides, since mean shift outlier models (MSOMs) are also efficient to detect outliers, we establish an equivalence between deletion models and MSOMs, which is not only suitable for fixed effects but also for random effects, and test statistics for outliers are then constructed. As a byproduct, we obtain the nonparametric “delete = replace” identity. Our influence diagnostics methods are illustrated through a simulated example and a real data set. [Copyright &y& Elsevier]

Background: Suboptimal health status (SHS) is the third state between good health and disease. SHS is the clinical or pre-disease status of psychosomatic disease and a major global public health challenge. Although its underlying causes remain unclear, lifestyle is one of the most important factors affecting health status.Methods: A cross-sectional survey was conducted at Renmin University of China in September of 2015. Data were collected from college freshmen using a questionnaire covering characteristics, lifestyle, nutrition status, and health status. A total of 6025 questionnaires were distributed during the study period, and 5344 completed responses were received.Results: The prevalence rates for the "healthy," "SHS," and "disease" groups of college freshmen were 46.7% (2433), 51.2% (2667), and 2.1% (111), respectively. It is notable that health status was significantly positively correlated with lifestyle (Spearman's r = 0.4435, p < 0.001). The multivariate Logistic regression results showed that students who were relatively younger and students from rural areas had a higher percentage of SHS. Good sleep quality (aOR = 0.650, 95%CI = 0.612-0.690), abundant physical exercise (aOR = 0.889, 95%CI = 0.845-0.933), and adequate nutrition intake (aOR = 0.868, 95%CI = 0.864-0.908) are negatively associated with SHS. Overuse of electronic devices (aOR = 1.066, 95%CI = 1.013-1.121), smoking (aOR = 1.824, 95%CI = 1.195-2.755), and weight loss (aOR = 1.255, 95%CI = 1.043-1.509) are positively associated with SHS.Conclusions: Poor lifestyle behaviors are associated with SHS. In particular, the overuse of electronic devices is one of underlying causes of SHS. By altering lifestyle behaviors for the better, the health statuses of these college freshmen can be effectively improved. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the associations of physical activity (PA) and screen time (ST) with physiological, psychological, and social health—particularly regarding effects on sleep quality—among Chinese college freshmen. A cross-sectional survey was conducted at Renmin University of China, in Beijing. A total of 5,233 students were surveyed in September 2015. Participants completed a self-report questionnaire on their demographic characteristics, tobacco and alcohol use, PA, ST, sleep quality, and health status. Multivariate logistic regression was performed to examine the independent and interactive associations between PA and ST with sleep quality and suboptimal health status. In total, 10.43%, 13.18%, and 13.26% of the 5,233 students had physiological, psychological, and social suboptimal health status, respectively. The prevalence of poor sleep quality was 37.94%. High ST and high PA were significantly associated with physiological suboptimal health status (aOR = 1.39, 95% CI: 1.16–1.68, and aOR = 0.55, 95% CI: 0.45–0.71), psychological suboptimal health status (aOR = 1.43, 95% CI: 1.21–1.69, and aOR = 0.57, 95% CI: 0.47–0.69), social suboptimal health status (aOR = 1.27, 95% CI: 1.08–1.50, and aOR = 0.63, 95% CI: 0.52–0.77), and poor sleep quality (aOR = 1.20, 95% CI: 1.03–1.39, and aOR = 0.64, 95% CI: 0.55–0.76). Additionally, low ST and high PA were interactively negatively associated with poor sleep quality (aOR = 0.56, 95% CI: 0.45–0.70), physiological suboptimal health status (aOR = 0.49, 95% CI: 0.40–0.59), psychological suboptimal health status (aOR = 0.48, 95% CI: 0.39–0.58), and social suboptimal health status (aOR = 0.49, 95% CI: 0.40–0.59). These findings suggested there are independent and interactive associations of low ST and high PA with poor sleep quality and suboptimal health status among Chinese college freshmen. [ABSTRACT FROM AUTHOR]

In multiple hypothesis test, an important problem is estimating the proportion of true null hypotheses. Existing methods are mainly based on thep-values of the single tests. In this paper, we propose two new estimations for this proportion. One is a natural extension of the commonly used methods based onp-values and the other is based on a mixed distribution. Simulations show that the first method is comparable with existing methods and performs better under some cases. And the method based on a mixed distribution can get accurate estimators even if the variance of data is large or the difference between the null hypothesis and alternative hypothesis is very small. [ABSTRACT FROM PUBLISHER]

The partial linear regression model is wildly used due to its well established theories, flexibility and easy interpretation. This paper aims to investigate the specification test of nonparametric component in partial linear model with response missing at random. Two quadratic conditional moment tests are proposed and both two test statistics own limiting normal distributions when nonparametric component is correctly specified. Our tests’ virtue is that p -values can be easily determined based on limiting null distributions which are intractable for existing tests. The tests can detect the alternative hypotheses distinct from the null hypothesis at the optimal nonparametric rate for local smoothing-based methods. Simulation studies reveal that our tests can control type I error well and have excellent power performance. A HIV clinical trial real data is analyzed for illustrating our methods. [ABSTRACT FROM AUTHOR]

Multiple test based on familywise error rate is a popular problem in statistical inference as testing the null hypothesisH0=H1∩H2∩···∩Hnis true versus the alternative that at least one hypothesis inH1,H2, … ,Hnis false. Classical tests include the Bonferroni test and the Simes test. So far, the most efficient methods for this problem are known as the combinedp-value tests, such as the Fisher's product test, the truncated product method, the rank truncated product test, the adaptive rank truncated product (ARTP) method and Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test that extends the ARTP method. Our method is based on Zhang et al.’s [A combinedp-value test for multiple hypothesis testing. J Stat Plan Inference. 2013;143:764–770] test and modifies it by using different critical percentile parameter τjfor the statisticwith eachj=1, … ,n. Simulation studies show that the sizes of our test are stable at the significance level and the powers are superior to commonly used methods. [ABSTRACT FROM PUBLISHER]

The Wilcoxon–Mann–Whitney test is designed to test homogeneity of two random samples in the univariate case. It is very powerful to detect location shifts yet may lose power completely when there exist scale differences. We generalize the classic Wilcoxon–Mann–Whitney test through using pairwise distances of all observations. The generalized test can be readily used even when the random observations are multivariate. It is also very powerful in the presence of scale differences. The generalized test is in spirit to compare difference between the distribution functions of two random samples. It is m n / (m + n) -consistent under the strong null and local alternatives, and root- m n / (m + n) -consistent under fixed alternatives, where m , n stand for the respective sizes of the two random samples. The power of the generalized test is asymptotically independent of m / n , the size ratio of the two random samples. This indicates that the generalized test has nontrivial power as long as the sample sizes are not extremely unbalanced. We demonstrate the theoretical properties of our improved rank-based two-sample test through comprehensive numerical studies. [ABSTRACT FROM AUTHOR]

Background: Recurrence continues to place significant burden on patients and tuberculosis programmes worldwide, and previous studies have rarely provided analysis in negative recurrence cases. We characterized the epidemiological features of recurrent pulmonary tuberculosis (PTB) patients, estimated its probability associated with different bacteriology results and risk factors.Methods: Using 2005-2018 provincial surveillance data from Henan, China, where the permanent population approximately were 100 million, we described the epidemiological and bacteriological features of recurrent PTB. The Kaplan-Meier method and Cox proportional hazard models, respectively, were used to estimate probability of recurrent PTB and risk factors.Results: A total of 7143 (1.5%) PTB patients had recurrence, and of 21.1% were bacteriological positive on both laboratory tests (positive-positive), and of 34.9% were negative-negative. Compared with bacteriological negative recurrent PTB at first episodes, the bacteriological positive cases were more male (81.70% vs 72.79%; P < 0.001), higher mortality risk (1.78% vs 0.92%; P = 0.003), lower proportion of cured or completed treatment (82.81% vs 84.97%; P = 0.022), and longer time from onset to end-of-treatment. The probability of recurrence was higher in bacteriological positive cases than those in bacteriological negative cases (0.5% vs 0.4% at 20 months; P < 0.05).Conclusions: Based on patient's epidemiological characteristics and bacteriological type, it was necessary to actively enact measures to control their recurrent. [ABSTRACT FROM AUTHOR]

Birnbaum–Saunders (BS) distribution is widely used in reliability applications to model failure times. For several samples from possible different BS distributions, to prevent wrong conclusions in any further analysis, it is of importance to accompany a formal comparison for characteristic quantities of the distributions, including mean, quantile and reliability function difference. To this end, two test statistics, which are respectively based on the exact generalizedp-value approach and the Delta method, are proposed and their behaviours are investigated. Simulation studies are carried out to examine the size and power performance of the newly proposed statistics. An interesting phenomenon is that in the finite sample simulations we conduct, the Delta method-based test almost uniformly outperforms the generalizedp-value-based test although its sampling null distribution is simulated by Monte Carlo method. This might suggest that the sampling null distribution of the Delta method-based test statistic would have a fast convergence to its limit. The tests are also applied to analyse a real example on the fatigue life of 6061-T6 aluminium coupons for illustration. [ABSTRACT FROM AUTHOR]

Due to the strikingly resemblance to the normal theory and inference methods, the inverse Gaussian (IG) distribution is commonly applied to model positive and right-skewed data. As the shape parameter in the IG distribution is greatly related to other important quantities such as the mean, skewness, kurtosis and the coefficient of variation, it plays an important role in distribution theory. This paper focuses on testing the equality of shape parameters in several inverse Gaussian distributions. Three tests are suggested: the exact generalized inference-based test, the asymptotic test and a test that is based on parametric bootstrap approximation. Simulation studies are undertaken to examine the performances of the these methods, and three real data examples are analyzed for illustration. [ABSTRACT FROM AUTHOR]

Background: This study explored the effect of a continuous mitigation and containment strategy for coronavirus disease 2019 (COVID-19) on five vector-borne diseases (VBDs) in China from 2020 to 2021. Methods: Data on VBDs from 2015 to 2021 were obtained from the National Health Commission of the People's Republic of China, and the actual trend in disease activity in 2020–2021 was compared with that in 2015–2019 using a two-ratio Z-test and two proportional tests. Similarly, the estimated trend in disease activity was compared with the actual trend in disease activity in 2020. Results: There were 13,456 and 3684 average yearly cases of VBDs in 2015–2019 and 2020, respectively. This represents a decrease in the average yearly incidence of total VBDs of 72.95% in 2020, from 0.9753 per 100,000 population in 2015–2019 to 0.2638 per 100,000 population in 2020 (t = 75.17, P < 0.001). The observed morbidity rates of the overall VBDs were significantly lower than the predicted rates (47.04% reduction; t = 31.72, P < 0.001). The greatest decline was found in dengue, with a 77.13% reduction (observed rate vs predicted rate: 0.0574 vs. 0.2510 per 100,000; t = 41.42, P < 0.001). Similarly, the average yearly mortality rate of total VBDs decreased by 77.60%, from 0.0064 per 100,000 population in 2015–2019 to 0.0014 per 100,000 population in 2020 (t = 6.58, P < 0.001). A decreasing trend was also seen in the monthly incidence of total VBDs in 2021 compared to 2020 by 43.14% (t = 5.48, P < 0.001). Conclusions: The results of this study verify that the mobility and mortality rates of VBDs significantly decreased from 2015–2019 to 2020–2021, and that they are possibly associated to the continuous COVID-19 mitigation and contamination strategy implemented in China in 2020–2021. [ABSTRACT FROM AUTHOR]

Outbreaks of acute hemorrhagic conjunctivitis (AHC) are associated with a high disease burden. In this study, we investigated the association between enhanced public health intervention and the incidence of AHC during the COVID-19 pandemic in China. A total of 212,526 AHC cases were reported in China during 2015–2020. The overall yearly incidence rate and number of AHC cases decreased by 23.08% and 22.15%, respectively, during the COVID-19 epidemic, compared with the previous 5 years (all p < 0.001). Significant reductions in AHC incidence were found both during the emergency period and after the relaxation of emergency measures in 2020 compared to the previous 5 years (22.22% and 28.00% reduction, respectively; p < 0.001). Enhanced public health initiatives during the COVID-19 pandemic in China were therefore associated with lower transmission of pathogens causing AHC. [ABSTRACT FROM AUTHOR]

In this paper, we use the empirical likelihood method to make inferences for the coefficient difference of a two-sample linear regression model with missing response data. The commonly used empirical likelihood ratio is not concave for this problem, so we append a natural and well-explained condition to the likelihood function and propose three types of restricted empirical likelihood ratios for constructing the confidence region of the parameter in question. It can be demonstrated that all three empirical likelihood ratios have, asymptotically, chi-squared distributions. Simulation studies are carried out to show the effectiveness of the proposed approaches in aspects of coverage probability and interval length. A real data set is analysed with our methods as an example. [ABSTRACT FROM AUTHOR]

One of the most basic and important problems in statistical inference is the construction of the confidence interval (CI). In this paper, we propose a novel CI for a binomial proportion by modifying the midpoint of the score interval. The proposed modified interval can solve the ‘downward spikes’ problem of the score interval without enlarging the interval length. Simulation studies are carried out to illustrate the performance of the modified interval. With regard to the criterions of coverage probability, mean absolute error and expected length, our method is competitive among the several commonly used methods for constructing a CI. A real data example is also presented to show the application of our method. [ABSTRACT FROM AUTHOR]

Testing for homogeneity of two random vectors is a fundamental problem in statistics. In the past two decades, numerous efforts have been made to detect heterogeneity when the random vectors are multivariate or even high dimensional. Due to the "curse of dimensionality", existing tests based on Euclidean distance may fail to capture the overall homogeneity in high-dimensional settings while can only capture the moment discrepancy. To address this issue, we propose a fully nonparametric test for homogeneity of two random vectors. Our method involves randomly selecting two subspaces consisting of components of the vectors, projecting the subspaces onto one-dimensional spaces, respectively, and constructing the test statistic using the Cramér–von Mises distance of the projections. To enhance the performance, we repeatedly implement this procedure to construct the final test statistic. Theoretically, if the replication time tends to infinity, we can avoid potential power loss caused by lousy directions. Owing to the U -statistic theory, the asymptotic null distribution of our proposed test is standard normal, regardless of the parent distributions of the random samples and the relationship between data dimensions and sample sizes. As a result, no re-sampling procedure is needed to determine critical values. The empirical size and power of the proposed test are demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

Two-stage design is a well-known cost-effective way for conducting biomedical studies when the exposure variable is expensive or difficult to measure. Recent research development further allowed one or both stages of the two-stage design to be outcome dependent on a continuous outcome variable. This outcome-dependent sampling feature enables further efficiency gain in parameter estimation and overall cost reduction of the study (e.g. Wang, X. and Zhou, H., 2010. Design and inference for cancer biomarker study with an outcome and auxiliary-dependent subsampling. Biometrics 66, 502-511; Zhou, H., Song, R., Wu, Y. and Qin, J., 2011. Statistical inference for a two-stage outcome-dependent sampling design with a continuous outcome. Biometrics 67, 194-202). In this paper, we develop a semiparametric mixed effect regression model for data from a two-stage design where the second-stage data are sampled with an outcome-auxiliary-dependent sample (OADS) scheme. Our method allows the cluster- or center-effects of the study subjects to be accounted for. We propose an estimated likelihood function to estimate the regression parameters. Simulation study indicates that greater study efficiency gains can be achieved under the proposed two-stage OADS design with center-effects when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a dataset from the Collaborative Perinatal Project. [ABSTRACT FROM AUTHOR]

Objective: To quantitatively evaluate the effectiveness of Fangcang shelter hospitals, designated hospitals, and the time interval from illness onset to diagnosis toward the prevention and control of the COVID-19 epidemic.Methods: We used SEIAR and SEIA-CQFH warehouse models to simulate the two-period epidemic in Wuhan and calculate the time dependent basic reproduction numbers (BRNs) of symptomatic infected individuals, asymptomatic infected individuals, exposed individuals, and community-isolated infected individuals. Scenarios that varied in terms of the maximum numbers of open beds in Fangcang shelter hospitals and designated hospitals, and the time intervals from illness onset to hospitals visit and diagnosis were considered to quantitatively assess the optimal measures.Results: The BRN decreased from 4.50 on Jan 22, 2020 to 0.18 on March 18, 2020. Without Fangcang shelter hospitals, the cumulative numbers of cases and deaths would increase by 18.58 and 51.73%, respectively. If the number of beds in the designated hospitals decreased by 1/2 and 1/4, the number of cumulative cases would increase by 178.04 and 92.1%, respectively. If the time interval from illness onset to hospital visit was 4 days, the number of cumulative cases and deaths would increase by 2.79 and 6.19%, respectively. If Fangcang shelter hospitals were not established, the number of beds in designated hospitals reduced 1/4, and the time interval from visiting hospitals to diagnosis became 4 days, the cumulative number of cases would increase by 268.97%.Conclusion: The declining BRNs indicate the high effectiveness of the joint measures. The joint measures led by Fangcang shelter hospitals are crucial and need to be rolled out globally, especially when medical resources are limited. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a nonparametric independence screening method for sparse ultra-high dimensional generalized varying coefficient models with longitudinal data. Our methods combine the ideas of sure independence screening (SIS) in sparse ultra-high dimensional generalized linear models and varying coefficient models with the marginal generalized estimating equation (GEE) method, called NIS-GEE, considering both the marginal correlation between response and covariates, and the subject correlation for variable screening. The corresponding iterative algorithm is introduced to enhance the performance of the proposed NIS-GEE method. Furthermore it is shown that, under some regularity conditions, the proposed NIS-GEE method enjoys the sure screening properties. Simulation studies and a real data analysis are used to assess the performance of the proposed method. [ABSTRACT FROM AUTHOR]

As a nonparametric randomness test, the positive and negative runs test is widely used in practice due to the simplicity of its procedures. The test can lose efficiency if the alternative distribution is symmetrical at 0.5. In addition, the test can only be applied to test the randomness of a sequence from the uniform distribution. In this paper, we introduce an adaptive positive and negative runs test method to maximize the power function by choosing the optimal cut point. Also, the test is extended to check the randomness of a sequence generated from any other given distributions. Furthermore, we derive the exact distribution and obtain the asymptotical critical values of the proposed test statistics. Compared with the existed test, the efficiency of the proposed adaptive positive and negative runs test is competitive through simulation study. [ABSTRACT FROM AUTHOR]