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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]

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]

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]

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]

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]

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]

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]

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]

Global climate change could have potential impact on enterovirus (EV)-induced infectious diseases. However, the environmental factors promoting acute hemorrhagic conjunctivitis (AHC) circulation remain inconclusive. This study aimed to quantify the relationship between the environment and AHC. We retrieved the monthly counts and incidence of AHC, meteorological variables and air quality in mainland China between 2013 and 2018. Exposure risks were evaluated by multivariate distributed lag nonlinear models. A total of 219,599 AHC cases were reported in 31 provinces of China, predominantly in southern and central China, seasonally increased in summer. AHC incidence increased by 7% between 2013 and 2018, from 2.6873 to 2.7570 per 100,000 people. A moderate positive correlation was seen between AHC and monthly mean temperature, relative humidity (RH) and precipitation. Each unit increment was associated with a relative risk for AHC of 1.058 at 17°-32 °C at lag 0 months, 1.017 at 65–71% RH at lag 1.4 months, and 1.039 at 400–569 mm at lag 2.4 months. By contrast, a negative correlation was seen between monthly ambient NO 2 and AHC. Long-term exposure to higher mean temperature, RH and precipitation were associated with an increased risk of AHC. The general public, especially susceptible populations, should pay close attention to weather changes and take protective measures in advance to any AHC outbreak as the above situations occur. [ABSTRACT FROM AUTHOR]