Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional l...Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional latent structure has been of great interest for statisticians.To this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction subspaces.The first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE method.The asymptotic properties of both methods are derived under mild conditions.Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.展开更多
In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to sele...In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.展开更多
基金supported by the National Natural Science Foundation of China(Grant NO.12301377,11971208,92358303)the National Social Science Foundation of China(Grant NO.21&ZD152)+4 种基金the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province(Grant No.20224ACB211003)Jiangxi Provincial National Natural Science Foundation(Grant NO.20232BAB211014)the Science and technology research project of the Education Department of Jiangxi Province(Grant No.GJJ210535)the opening funding of Key Laboratory of Data Science in Finance and Economicsthe innovation team funding of Digital Economy and Industrial Development,Jiangxi University of Finance and Economics。
文摘Tensor data have been widely used in many fields,e.g.,modern biomedical imaging,chemometrics,and economics,but often suffer from some common issues as in high dimensional statistics.How to find their low-dimensional latent structure has been of great interest for statisticians.To this end,we develop two efficient tensor sufficient dimension reduction methods based on the sliced average variance estimation(SAVE)to estimate the corresponding dimension reduction subspaces.The first one,entitled tensor sliced average variance estimation(TSAVE),works well when the response is discrete or takes finite values,but is not■consistent for continuous response;the second one,named bias-correction tensor sliced average variance estimation(CTSAVE),is a de-biased version of the TSAVE method.The asymptotic properties of both methods are derived under mild conditions.Simulations and real data examples are also provided to show the superiority of the efficiency of the developed methods.
基金supported by National Natural Science Foundation of China (Grant No. 10771015)
文摘In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.
