We,in this paper,investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random.In particular,based on suffic...We,in this paper,investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random.In particular,based on sufficient dimension reduction technique,we construct three empirical log-likelihood ratios for the quantile difference between two samples by using inverse probability weighting imputation,regression imputation as well as augmented inverse probability weighting imputation,respectively,and prove their asymptotic distributions.At the same time,we give a test to check whether two populations have the same distribution.A simulation study is carried out to investigate finite sample behavior of the proposed methods too.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 National Natural Science Foundation of China(Grant No.12071348)National Social Science Foundation of China(Grant No.17BTJ032)。
文摘We,in this paper,investigate two-sample quantile difference by empirical likelihood method when the responses with high-dimensional covariates of the two populations are missing at random.In particular,based on sufficient dimension reduction technique,we construct three empirical log-likelihood ratios for the quantile difference between two samples by using inverse probability weighting imputation,regression imputation as well as augmented inverse probability weighting imputation,respectively,and prove their asymptotic distributions.At the same time,we give a test to check whether two populations have the same distribution.A simulation study is carried out to investigate finite sample behavior of the proposed methods too.
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.
