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Asymptotic Theory for Estimation of Error Distribution in linear model

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Science China Mathematics 1993年第4期36卷 408-419页

作者：柴根象李竹渝 Department of Mathematics Sichuan University Chengdu 610064 PRC

For a linear model, let the error sequence be i.i.d, with common unknown density f(x), and (x) be a nonparametric estimator of f(x) based on the residuals. In this paper, on the basis of [1], we establish the L_1-norm consistency, asymptotic normality and law of iterated logarithm for (x) under general condition. These results bring the asymptotic theory for estimation of error distributions to completion.

关键词： linear model error distribution L_1-norm eonsisteney asymptotic normality law of iterated logarithm.

Bootstrap Approximation to the Distribution of M-estimates in a linear model

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Acta Mathematica Sinica,English Series 2004年第1期20卷 93-104页

作者： XiaoMingWANG WangZHOU DepartmentofStatistics ShanghaiUniversityofFinanceandEconomicsShanghai200433P.R.China DepartmentofMathematics HongKongUniversityofScienceandTechnologyHongKong

The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.

关键词： linear model M-estimate linear representation Bootstrap approximation Normal approximation Randomly weighted approximation

Adaptive Unified Biased Estimators of Parameters in linear model

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Acta Mathematicae Applicatae Sinica 2004年第3期20卷 425-432页

作者： HuYang Li-xingZhu CollegeofScience ChongqingUniversitychongqing400044China DepartmentofStatisticsandActuarialScience TheUniversityofHongKong

To tackle multi collinearity or ill-conditioned design matrices in linear models, adaptive biased estimators such as the time-honored Stein estimator, the ridge and the principal component estimators have been studied intensively. To study when a biased estimator uniformly outperforms the least squares estimator, some sufficient conditions are proposed in the literature. In this paper, we propose a unified framework to formulate a class of adaptive biased estimators. This class includes all existing biased estimators and some new ones. A sufficient condition for outperforming the least squares estimator is proposed. In terms of selecting parameters in the condition, we can obtain all double-type conditions in the literature.

关键词： Least squares estimator linear model sufficient condition adaptive unified biased estimator

STRONG CONSISTENCY OF M ESTIMATOR IN linear model FOR NEGATIVELY ASSOCIATED SAMPLES

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Journal of Systems Science & Complexity 2006年第4期19卷 592-600页

作者： Qunying WU Department of Maths and Physics Guilin University of Technology Ouilin 541004 China.

This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） t... 详细信息

关键词： linear model M estimator negatively associated sample strong consistency.

Group screening for ultra-high-dimensional feature under linear model

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Statistical Theory and Related Fields 2020年第1期4卷 43-54页

作者： Yong Niu Riquan Zhang Jicai Liu Huapeng Li School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China Department of Mathematics and Physics Hefei UniversityHefeiPeople’s Republic of China Department of Mathematics Shanghai Normal UniversityShanghaiPeople’s Republic of China

Ultra-high-dimensional data with grouping structures arise naturally in many contemporary statistical problems,such as gene-wide association studies and the multi-factor analysis-of-variance(ANOVA).To address this issue,we proposed a group screening method to do variables selection on groups of variables in linear *** group screening method is based on a working independence,and sure screening property is also established for our *** enhance the finite sample performance,a data-driven thresholding and a two-stage iterative procedure are *** the best of our knowledge,screening for grouped variables rarely appeared in the literature,and this method can be regarded as an important and non-trivial extension of screening for individual *** extensive simulation study and a real data analysis demonstrate its finite sample performance.

关键词： Ultra-high-dimensional group screening linear model sure screening property

Adaptive Unified Biased Estimators of Parameters in linear model

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Acta Mathematicae Applicatae Sinica 2004年第3期 71-78页

作者： Hu Yang~1 Li-xing Zhu~(2,3)1 College of Science,Chongqing University,chongqing 400044,China(E-mail:yh@***)2 Department of Statistics and Actuarial Science,The University of Hong Kong3 Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China

To tackle multi collinearity or ill-conditioned design matrices in linear models,adaptive biasedestimators such as the time-honored Stein estimator,the ridge and the principal component estimators havebeen studied *** study when a biased estimator uniformly outperforms the least squares estimator,some sufficient conditions are proposed in the *** this paper,we propose a unified framework toformulate a class of adaptive biased *** class includes all existing biased estimators and some newones.A sufficient condition for outperforming the least squares estimator is *** terms of selectingparameters in the condition,we can obtain all double-type conditions in the literature.

关键词： Least squares estimator linear model sufficient coadition adaptive unified biased estimator

Further research on simple projection prediction under a general linear model

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Frontiers of Mathematics in China 2024年第5期19卷 255-275页

作者： Bo JIANG Luping WANG Yongge TIAN College of Mathematics and Information Science Shandong Technology and Business UniversityYantai 264005China College of Business and Economics Shanghai Business SchoolShanghai 201400China

linear model is a kind of important model in *** estimation and prediction of unknown parameters in the model is a basic problem in statistical *** to different evaluation criteria,different forms of predictors are *** simple projection prediction(SPP)boasts simple form while the best linear unbiased prediction(BLUP)enjoys very excellent ***,the relationship between the two predictors are *** give the necessary and sufficient conditions for the equality of SPP and ***,we study the robustness of SPP and BLUP with respect to covariance matrix and illustrate the application of equivalence conditions by use of error uniform correlation models.

关键词： linear model SPP BLUP equivalence robustness

THE OPTIMAL DESIGN BASED ON RELIABILITY OF WATER DISTRIBUTION SYSTEM BY linear model

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Journal of Hydrodynamics 1997年第1期9卷 63-69页

作者： Xu Zu-xin, Liu Sui-qingTongji University, Shanghai 200092,P. R. ChinaR. GuercioDepart. of Hydraulics,Transportation and highway,University of Rome,Rome,Italy

In this paper, a new technique are developed for optimal design of water distribution system besed on reliability. It applies a linear programming algorithm to the optimal design based on reliability. Within a small optimal search step range,the objective function and constraints can be expressed in the first order Taylor-expanding form,and three sub-models (a steady-state simulation model, a reliability model and a linear optimization model) are linked each in optimal searches. Thus, a traditional non linear problem can be solved by a linear model, the computing burden is significantly decreased. Therefore, the linear optimal model developed by the paper has more practical significance.

关键词： linear model reliability,optimal design water distribution system

A Male’s Girth linear model Based on 2-Dimensional Pictures Data

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A Male’s Girth Linear Model Based on 2-Dimensional Pictures...