In this study,we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample.The test statistic can be formulated such that Ustatistic the...In this study,we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample.The test statistic can be formulated such that Ustatistic theory can be applied to it.Although the limiting null distribution of the statistic is complicated,we can derive a computationally feasible bootstrap approximation for such a distribution;the validity of the introduced bootstrap algorithm is proven.The test can detect any local alternatives that are different from the null at a nearly optimal rate in hypothesis testing.The convergence rate of this test statistic does not depend on the dimension of the covariates,which significantly alleviates the impact of dimensionality.We provide three simulation studies and a real-data example to evaluate the performance of the test and demonstrate its applications.展开更多
In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed fi...In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.展开更多
When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of ...When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.展开更多
基金supported by Shenzhen Sci-Tech Fund(Grant No.JCYJ 20170307110329106)the Natural Science Foundation of Guangdong Province of China(Grant No.2016A030313856)+1 种基金National Natural Science Foundation of China(Grant Nos.11701034,11601227,11871263 and 11671042)the University Grants Council of Hong Kong。
文摘In this study,we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample.The test statistic can be formulated such that Ustatistic theory can be applied to it.Although the limiting null distribution of the statistic is complicated,we can derive a computationally feasible bootstrap approximation for such a distribution;the validity of the introduced bootstrap algorithm is proven.The test can detect any local alternatives that are different from the null at a nearly optimal rate in hypothesis testing.The convergence rate of this test statistic does not depend on the dimension of the covariates,which significantly alleviates the impact of dimensionality.We provide three simulation studies and a real-data example to evaluate the performance of the test and demonstrate its applications.
基金National Natural Science Foundation of China(Grant Nos.11901006 and 11601008)Natural Science Foundation of Anhui Province(Grant No.1908085QA06)。
文摘In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.
基金supported by the National Natural Science Foundation of China under Grant No.11271368the Major Program of Beijing Philosophy and Social Science Foundation of China under Grant No.15ZDA17+3 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20130004110007the Key Program of National Philosophy and Social Science Foundation under Grant No.13AZD064the Fundamental Research Funds for the Central Universities,and the Research Funds of Renmin University of China under Grant No.15XNL008the Project of Flying Apsaras Scholar of Lanzhou University of Finance & Economics
文摘When dealing with regression analysis,heteroscedasticity is a problem that the authors have to face with.Especially if little information can be got in advance,detection of heteroscedasticity as well as estimation of statistical models could be even more difficult.To this end,this paper proposes a quantile difference method(QDM) that can effectively estimate the heteroscedastic function.This method,being completely free from the estimation of mean regression function,is simple,robust and easy to implement.Moreover,the QDM method enables the detection of heteroscedasticity without any restrictions on error terms,consequently being widely applied.What is worth mentioning is that based on the proposed approach estimators of both mean regression function and heteroscedastic function can be obtained.In the end,the authors conduct some simulations to examine the performance of the proposed methods and use a real data to make an illustration.
