Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness pr...Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property(the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point(FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one—the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.展开更多
This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors de...This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.展开更多
The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test statistics are shown to have standard chi- squared distribution...The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test statistics are shown to have standard chi- squared distribution asymptotically when there is no serial correlation in the error terms. To illustrate their finite sample properties, simulation experiments, as well as a real data example, are also provided. It is revealed that the finite sample performances of the proposed test statistics are satisfactory in terms of both estimated sizes and powers.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11601197,11461029,71463020,61263014 and 61563018),National Natural Science Foundation of China(Grant Nos.General program 11171331 and Key program 11331011)National Science Foundation of Jiangxi Province(Grant Nos.20161BAB201024,20142BAB211014,20143ACB21012 and 20151BAB211016)+3 种基金the Key Science Fund Project of Jiangxi Provincial Education Department(Grant Nos.GJJ150439,KJLD13033 and KJLD14034)the National Science Fund for Distinguished Young Scholars in China(Grant No.10725106)a grant from the Key Lab of Random Complex Structure and Data Science,Chinese Academy of SciencesNatural Science Foundation of Shenzhen University
文摘Tukey's halfspace median(HM), servicing as the multivariate counterpart of the univariate median,has been introduced and extensively studied in the literature. It is supposed and expected to preserve robustness property(the most outstanding property) of the univariate median. One of prevalent quantitative assessments of robustness is finite sample breakdown point(FSBP). Indeed, the FSBP of many multivariate medians have been identified, except for the most prevailing one—the Tukey's halfspace median. This paper presents a precise result on FSBP for Tukey's halfspace median. The result here depicts the complete prospect of the global robustness of HM in the finite sample practical scenario, revealing the dimension effect on the breakdown point robustness and complimenting the existing asymptotic breakdown point result.
基金supported by the National Natural Science Foundation of China(No.11271286)the Specialized Research Fund for the Doctor Program of Higher Education of China(No.20120072110007)a grant from the Natural Sciences and Engineering Research Council of Canada
文摘This paper deals with the conditional quantile estimation based on left-truncated and right-censored data.Assuming that the observations with multivariate covariates form a stationary α-mixing sequence,the authors derive the strong convergence with rate,strong representation as well as asymptotic normality of the conditional quantile estimator.Also,a Berry-Esseen-type bound for the estimator is established.In addition,the finite sample behavior of the estimator is investigated via simulations.
基金supported by CCNU under Grant No.09A01002the SCR of Chongqing Municipal Education Commission under Grant No.KJ110713the National Natural Science Foundation of China under Grant Nos.11101452 and 71172093
文摘The purpose of this paper is to test the underlying serial correlation in a partially linear single-index model. Under mild conditions, the proposed test statistics are shown to have standard chi- squared distribution asymptotically when there is no serial correlation in the error terms. To illustrate their finite sample properties, simulation experiments, as well as a real data example, are also provided. It is revealed that the finite sample performances of the proposed test statistics are satisfactory in terms of both estimated sizes and powers.
