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
To the Editor:Accumulating evidence has shown that the preclinical stage of Alzheimer’s disease(AD)(i.e.,asymptomatic amyloidosis)lasts for decades before the onset of cognitive symptoms,providing a large window for ...To the Editor:Accumulating evidence has shown that the preclinical stage of Alzheimer’s disease(AD)(i.e.,asymptomatic amyloidosis)lasts for decades before the onset of cognitive symptoms,providing a large window for early intervention.Amyloid pathology,the earliest pathological change associated with AD,can be detected in vivo with cerebrospinal fluid(CSF)analysis or positron emission tomography(PET),and its presence is necessary for the diagnosis of preclinical AD(pre-AD).However,both PET scans and CSF analyses are expensive,hampering their use in large-scale screening.Thus,blood-based biomarkers are desirable alternatives,as they are cost-effective and not invasive.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 grants from the National Natural Science Foundation of China(Nos.82020108013 and 82001773)National Key Research and Development Program of China(No.2022YFC24069004)+1 种基金Beijing Brain Initiative from Beijing Municipal Science&Technology Commission(No.Z201100005520018)STI2030-Major Projects(No.2022ZD0211800)
文摘To the Editor:Accumulating evidence has shown that the preclinical stage of Alzheimer’s disease(AD)(i.e.,asymptomatic amyloidosis)lasts for decades before the onset of cognitive symptoms,providing a large window for early intervention.Amyloid pathology,the earliest pathological change associated with AD,can be detected in vivo with cerebrospinal fluid(CSF)analysis or positron emission tomography(PET),and its presence is necessary for the diagnosis of preclinical AD(pre-AD).However,both PET scans and CSF analyses are expensive,hampering their use in large-scale screening.Thus,blood-based biomarkers are desirable alternatives,as they are cost-effective and not invasive.
