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Delete-group Jackknife Estimate in Partially Linear Regression Models with Heteroscedasticity

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Acta Mathematicae Applicatae Sinica 2003年第4期19卷 599-610页

作者： Jin-hong You Gemai Chen Department of Biostatistics University of North CarolinaChapel HillNC 27599-7420U.S.A.Department of Mathematics & StatisticsUniversity of Calgary CalgaryAlbertaCanada T2N 1N4

Consider a partially linear regression model with an unknown vector parameter , an unknown function g(·), and unknown heteroscedastic error variances. Chen, You[23] proposed a semiparametric generalized least squares estimator (SGLSE) for , which takes the heteroscedasticity into account to increase efficiency. For inference based on this SGLSE, it is necessary to construct a consistent estimator for its asymptotic covariance matrix. However, when there exists within-group correlation, the traditional delta method and the delete-1 jackknife estimation fail to offer such a consistent estimator. In this paper, by deleting grouped partial residuals a delete-group jackknife method is examined. It is shown that the delete-group jackknife method indeed can provide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations. This result is an extension of that in [21].

关键词： Partially linear regression model asymptotic variance heteroscedasticity delete-group jackknife semiparametric generalized least squares estimator

Impact of sufficient dimension reduction in nonparametric estimation of causal effect

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Statistical Theory and Related Fields 2018年第1期2卷 89-95页

作者： Ying Zhang Jun Shao Menggang Yu Lei Wang Department of Statistics University of Wisconsin-MadisonMadisonWIUSA School of Statistics East China Normal UniversityShanghaiPeople’s Republic of China Department of Biostatistics and Medical Informatics University of Wisconsin-MadisonMadisonWIUSA Institute of Statistics and LPMC Nankai UniversityTianjinPeople’s Republic of China

We consider the estimation of causal treatment effect using nonparametric regression orinverse propensity weighting together with sufficient dimension reduction for searching lowdimensional covariate subsets. A special case of this problem is the estimation of a responseeffect with data having ignorable missing response values. An issue that is not well addressedin the literature is whether the estimation of the low-dimensional covariate subsets by sufficient dimension reduction has an impact on the asymptotic variance of the resulting causaleffect estimator. With some incorrect or inaccurate statements, many researchers believe thatthe estimation of the low-dimensional covariate subsets by sufficient dimension reduction doesnot affect the asymptotic variance. We rigorously establish a result showing that this is nottrue unless the low-dimensional covariate subsets include some covariates superfluous for estimation, and including such covariates loses efficiency. Our theory is supplemented by somesimulation results.

关键词： asymptotic variance causal treatment effect nonparametric regression or propensity weighting n^(1/2)-consistency

Multiple Objective Test Design for Accelerated Destructive Degradation Tests

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Journal of Donghua University(English Edition) 2015年第6期32卷 954-956页

作者：黄硕杨军彭锐赵宇 School of Reliability and Systems Engineering Beihang University Dongling School of Economics and Management University of Science and Technology

Accelerated destructive degradation tests(ADDTs)are powerful to provide reliability information in the degradation processes with destructive *** order to carry out an ADDT efficiently,both the estimation precision of parameters and the test cost should be *** the basis of the given degradation model and failure criterion,a multiple-objective optimization model for the design of ADDTs is *** constrains of the maximum measurement time,the total sample size and the number of stress levels,a comprehensive target function is suggested to reflect both the precision of lifetime estimation and total cost,and the optimal test plan is obtained,which is composed by optimal choices for samples size,measurement frequency,and the number of measurements at each stress level.A real example is illustrated to demonstrate the implementation of the proposed approach.

关键词： accelerated destructive degradation tests(ADDTs) highly reliable products multiple objectives test cost asymptotic variance

Uncertainty Comparison Between Value-at-Risk and Expected Shortfall

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Communications in Mathematical Research 2024年第1期40卷 102-124页

作者： Qing Liu Weimin Liu Liang Peng Gengsheng Qin School of Statistics Jjiangxi University of Finance and EconomicsNanchangJiangxi 330013China Department of Mathematics and Statistics Georgia State UniversityAtlantaGA 30303USA Maurice R.Greenberg School of Risk Science Georgia State UniversityAtlantaGA 20303USA

Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk *** these two measures has been a hot debate,and most discussions focus on risk measure *** paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk *** and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.

关键词： α-mixing asymptotic variance expected shortfall Value-at-Risk

Nearly best linear estimates of logistic parameters based on complete ordered statistics

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Journal of Harbin Institute of Technology(New Series) 2001年第2期8卷 178-183页

作者：王承官吴从炘 Dept. of Mathematics Harbin Institute of Technology

Deals with the determination of the nearly best linear estimates of location and scale parameters of a logistic population, when both parameters are unknown, by introducing Blom’s semi empirical ’α,β correction’ into the asymptotic mean and covariance formulae with complete and ordered samples taken into consideration and various nearly best linear estimates established and points out the high efficiency of these estimators relative to the best linear unbiased estimators (BLUEs) and other linear estimators makes them useful in practice.

关键词： Estimation order statistics logistic distribution asymptotic variance

A Novel Approach to Optimal Input Signal Design for Data Driven Control

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A Novel Approach to Optimal Input Signal Design for Data Dri...