Pub Date : 2026-03-01Epub Date: 2025-11-14DOI: 10.1016/j.jmva.2025.105543
Runfei Luo , Anna Liu , Hao Dong , Yuedong Wang
Density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships, whereas a graphical structure can be used to build models for density estimation. We propose a semiparametric framework that models part of the density function nonparametrically using a smoothing spline ANOVA (SS ANOVA) model and the conditional density parametrically using a conditional Gaussian graphical model (cGGM). This flexible framework allows us to deal with high-dimensional data without the Gaussian assumption. We develop computationally efficient algorithms for estimation and provide theoretical guarantees for our procedure. Our experimental results show that the proposed framework outperforms both parametric and nonparametric baselines.
{"title":"Density and graph estimation with smoothing splines and conditional Gaussian graphical models","authors":"Runfei Luo , Anna Liu , Hao Dong , Yuedong Wang","doi":"10.1016/j.jmva.2025.105543","DOIUrl":"10.1016/j.jmva.2025.105543","url":null,"abstract":"<div><div>Density estimation and graphical models play important roles in statistical learning. The estimated density can be used to construct a graphical model that reveals conditional relationships, whereas a graphical structure can be used to build models for density estimation. We propose a semiparametric framework that models part of the density function nonparametrically using a smoothing spline ANOVA (SS ANOVA) model and the conditional density parametrically using a conditional Gaussian graphical model (cGGM). This flexible framework allows us to deal with high-dimensional data without the Gaussian assumption. We develop computationally efficient algorithms for estimation and provide theoretical guarantees for our procedure. Our experimental results show that the proposed framework outperforms both parametric and nonparametric baselines.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105543"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-17DOI: 10.1016/j.jmva.2025.105544
Jiajie Lu, Xiaohu Li
In this study, we investigate both sufficient and necessary conditions for bivariate skew-normal distributions to be stochastic arrangement increasing. The main results serve as either natural extension of or nice supplement to the characterization result of this property for bivariate normal distributions due to Cai and Wei (2015). Also, we generalize these results to multivariate skew-normal distributions. Numerical examples based on the theory and a real data are presented to illustrate the main results as well.
{"title":"Stochastic arrangement increasing property of skew-normal distributions","authors":"Jiajie Lu, Xiaohu Li","doi":"10.1016/j.jmva.2025.105544","DOIUrl":"10.1016/j.jmva.2025.105544","url":null,"abstract":"<div><div>In this study, we investigate both sufficient and necessary conditions for bivariate skew-normal distributions to be stochastic arrangement increasing. The main results serve as either natural extension of or nice supplement to the characterization result of this property for bivariate normal distributions due to Cai and Wei (2015). Also, we generalize these results to multivariate skew-normal distributions. Numerical examples based on the theory and a real data are presented to illustrate the main results as well.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105544"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105561
Shu-Yu Li , Han-Ying Liang , Bao-Hua Wang
We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.
{"title":"Varying-coefficient quantile regression with effect under panel data and missing observation","authors":"Shu-Yu Li , Han-Ying Liang , Bao-Hua Wang","doi":"10.1016/j.jmva.2025.105561","DOIUrl":"10.1016/j.jmva.2025.105561","url":null,"abstract":"<div><div>We, in this paper, focus on partial linear varying-coefficient quantile regression with fixed effects under panel data and missing observations, where the missing observations include either responses or covariates are missing at random. Under independent setting, we define estimators of the unknown parameter vector, varying-coefficient function and effect in the model, and discuss their large number properties. To use the information from within-subject correlations, we propose weighted estimators for the unknown amounts, where the weights are chosen based on mean and quantile regressions, respectively, by quadratic inference technique and empirical likelihood method. Under dependent assumption, we establish asymptotic normality of the weighted estimators. Meanwhile, we study hypothesis tests of the parameter, varying-coefficient function and effect, and prove asymptotic distributions of restricted estimators and test statistics of the parameter under null hypothesis and local alternative hypothesis, respectively. Also, oracle property of the parameter is considered. Simulation study and real data analysis are conducted to evaluate the performance of the proposed methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105561"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105566
Xueyan Huang, Rui Qiu, Zhou Yu
In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.
{"title":"Fréchet kNN-based sufficient dimension reduction","authors":"Xueyan Huang, Rui Qiu, Zhou Yu","doi":"10.1016/j.jmva.2025.105566","DOIUrl":"10.1016/j.jmva.2025.105566","url":null,"abstract":"<div><div>In this paper, we introduce two Fréchet inverse regression methods with kernel bandwidths determined by <span><math><mi>k</mi></math></span> nearest neighbors, designed to achieve sufficient dimension reduction for a metric space-valued response and Euclidean predictors. A key advantage of the proposals lies in their ability to effectively preserve the intrinsic information of the metric space-valued response. We establish the asymptotic normality of these methods through rigorous theoretical proofs. Additionally, simulations and a real data example are provided to validate the performance and practical applicability of the proposed methods.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105566"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105556
Claire Geldenhuys, Rene Ehlers, Andriette Bekker
An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.
{"title":"Type I multivariate Pólya-Aeppli distributions with applications","authors":"Claire Geldenhuys, Rene Ehlers, Andriette Bekker","doi":"10.1016/j.jmva.2025.105556","DOIUrl":"10.1016/j.jmva.2025.105556","url":null,"abstract":"<div><div>An extensive body of literature exists that specifically addresses the univariate case of zero-inflated count models. In contrast, research pertaining to multivariate models is notably less developed. We propose two new parsimonious multivariate models that can be used to model correlated multivariate overdispersed count data. Furthermore, for different parameter settings and sample sizes, various simulations are performed. In conclusion, we demonstrate the performance of the newly proposed multivariate candidates on two benchmark datasets, which surpasses that of several alternative approaches.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105556"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105572
Yongshuai Chen , Gongming Shi , Xiaomeng Yan, Baoxue Zhang
In this paper, we study the limiting distribution of Chen-Qin’s test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens–Fisher problem. We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distributions. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.
{"title":"On the two-sample Behrens–Fisher problem for high-dimensional data","authors":"Yongshuai Chen , Gongming Shi , Xiaomeng Yan, Baoxue Zhang","doi":"10.1016/j.jmva.2025.105572","DOIUrl":"10.1016/j.jmva.2025.105572","url":null,"abstract":"<div><div>In this paper, we study the limiting distribution of Chen-Qin’s test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens–Fisher problem. We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distributions. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105572"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145681890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105574
Yuan Liu , Yan-Yong Zhao , Noriszura Ismail , Razik Ridzuan Mohd Tajuddin , Yuchun Zhang
Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.
{"title":"Jump detection in single-index models with measurement error","authors":"Yuan Liu , Yan-Yong Zhao , Noriszura Ismail , Razik Ridzuan Mohd Tajuddin , Yuchun Zhang","doi":"10.1016/j.jmva.2025.105574","DOIUrl":"10.1016/j.jmva.2025.105574","url":null,"abstract":"<div><div>Measurement error regression is widely used in statistical modeling. When the regression function is discontinuous, the estimation and inference have become challenging. In this paper, we develop a jump detection framework for a single index model with measurement error. First, for the single index model with measurement error, the consistent estimator of the index coefficient is obtained by using both the SIMEX (simulation extrapolation) and estimation equation methods. Then, the one-sided kernel local linear method is used to construct the estimator of the nonparametric function and the estimator of the jump point. Under some regularity assumptions, the asymptotic properties of the resultant estimators are established. The finite sample performance of our methodologies is evaluated by numerical simulation, and finally they are used to analyze the effect of serum cholesterol level and age on male blood.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105574"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-28DOI: 10.1016/j.jmva.2025.105562
Jiajuan Liang , Peter M. Bentler , Yiwen Cao
Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.
{"title":"Testing multivariate normality for two-level structural equation models","authors":"Jiajuan Liang , Peter M. Bentler , Yiwen Cao","doi":"10.1016/j.jmva.2025.105562","DOIUrl":"10.1016/j.jmva.2025.105562","url":null,"abstract":"<div><div>Multivariate normality is a common assumption in the maximum likelihood analysis of two-level structural equation models. Under the normal assumption, the independence condition on level-1 observations is no longer satisfied. As a result, existing statistics for testing multivariate normality based independent observations cannot be directly used for the same purpose in two-level structural equation models. In this paper we tackle this problem by employing the theory of spherical matrix distributions and some properties of invariant statistics. A series of necessary tests are constructed from some existing invariant statistics with a balanced level-1 sample design. These necessary tests are applicable without requiring a large level-1 or level-2 sample size. A Monte Carlo study is carried out to demonstrate the performance of the proposed tests in the aspects of controlling type I error rates, the power against a departure from multivariate normality for level-1 variables, and the power against a departure from multivariate normality for level-2 variables. An application of the necessary tests to a practical data set is illustrated.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105562"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145616475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a -dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach—we search for mutually orthogonal unit directions which maximise the -Wasserstein distance of the empirical distribution of data-projections along these directions from a standard Gaussian. Under a generative model, where there is a underlying (unknown) low-dimensional non-Gaussian subspace, we prove rigorous statistical guarantees on the accuracy of approximating this unknown subspace by the directions found by our projection pursuit approach. Our results operate in the regime where the data dimensionality is comparable to the sample size, and thus supplement the recent literature on the non-feasibility of locating interesting directions via projection pursuit in the complementary regime where the data dimensionality is much larger than the sample size.
{"title":"Wasserstein projection pursuit of non-Gaussian signals","authors":"Satyaki Mukherjee , Soumendu Sundar Mukherjee , Debarghya Ghoshdastidar","doi":"10.1016/j.jmva.2025.105535","DOIUrl":"10.1016/j.jmva.2025.105535","url":null,"abstract":"<div><div>We consider the general dimensionality reduction problem of locating in a high-dimensional data cloud, a <span><math><mi>k</mi></math></span>-dimensional non-Gaussian subspace of interesting features. We use a projection pursuit approach—we search for mutually orthogonal unit directions which maximise the <span><math><mi>q</mi></math></span>-Wasserstein distance of the empirical distribution of data-projections along these directions from a standard Gaussian. Under a generative model, where there is a underlying (unknown) low-dimensional non-Gaussian subspace, we prove rigorous statistical guarantees on the accuracy of approximating this unknown subspace by the directions found by our projection pursuit approach. Our results operate in the regime where the data dimensionality is comparable to the sample size, and thus supplement the recent literature on the non-feasibility of locating interesting directions via projection pursuit in the complementary regime where the data dimensionality is much larger than the sample size.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105535"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2025-11-15DOI: 10.1016/j.jmva.2025.105526
Rou Zhong , Jingxiao Zhang , Chunming Zhang
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Loève expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure with the use of neural networks. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to a real-world data set to further demonstrate its superiority.
{"title":"Nonlinear functional principal component analysis using neural networks","authors":"Rou Zhong , Jingxiao Zhang , Chunming Zhang","doi":"10.1016/j.jmva.2025.105526","DOIUrl":"10.1016/j.jmva.2025.105526","url":null,"abstract":"<div><div>Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Loève expansion, which assumes a linear structure of the observed functional data. However, the assumption may not always be satisfied, and the FPCA method can become inefficient when the data deviates from the linear assumption. In this paper, we propose a novel FPCA method that is suitable for data with a nonlinear structure with the use of neural networks. We construct networks that can be applied to functional data and explore the corresponding universal approximation property. The main use of our proposed nonlinear FPCA method is curve reconstruction. We conduct a simulation study to evaluate the performance of our method. The proposed method is also applied to a real-world data set to further demonstrate its superiority.</div></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"212 ","pages":"Article 105526"},"PeriodicalIF":1.4,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145537559","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号