In order to study the reliability of the empirical estimation of joint shear strength by the JRC(joint roughness coefficient)-JCS(joint compressive strength) model,natural rock joints of dif-ferent lithologic char...In order to study the reliability of the empirical estimation of joint shear strength by the JRC(joint roughness coefficient)-JCS(joint compressive strength) model,natural rock joints of dif-ferent lithologic characteristics and different sizes were selected as samples,and their shear strengths under dry and saturated conditions were measured by direct shear test and compared to those esti-mated by the JRC-JCS model.Comparison results show that for natural rock joints with joint surfaces closely matched,the average relative error of joint shear strength between empirical estimation and direct shear test is 9.9%;the reliability of the empirical estimation of joint shear strength by the JRC-JCS model is good under both dry and saturated conditions if the JRC is determined accounting for directional statistical measurements,scale effect and surface smoothing during shearing.However,for natural rock joints with joint surfaces mismatched,the average relative error of joint shear strength between empirical estimation and direct shear test is 39.9%;the reliability of empirical estimation of joint shear strength by the JRC-JCS model is questionable under both dry and saturated conditions.展开更多
In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares...In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion.展开更多
In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.展开更多
For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
A control integration with the normal solar constant and one with it increased by 2.5% in the National Center for Atmospheric Research (NCAR) coupled atmosphere-ocean Climate System Model were conducted to see how w...A control integration with the normal solar constant and one with it increased by 2.5% in the National Center for Atmospheric Research (NCAR) coupled atmosphere-ocean Climate System Model were conducted to see how well the actual realized global warming could be predicted just by analysis of the control results. This is a test, within a model context, of proposals that have been advanced to use knowledge of the present day climate to make "empirical" estimates of global climate sensitivity. The scaling of the top-of-the-atmosphere infrared flux and the planetary albedo as functions of surface temperature was inferred by examining four different temporal and geographical variations of the control simulations. Each of these inferences greatly overestimates the climate sensitivity of the model, largely because of the behavior of the cloud albedo. In each inference the control results suggest that cloudiness and albedo decrease with increasing surface temperature. However, the experiment with the increased solar constant actually has higher albedo and more cloudiness at most latitudes. The increased albedo is a strong negative feedback, and this helps account for the rather weak sensitivity of the climate in the NCAR model. To the extent that these model results apply to the real world, they suggest empirical evaluation of the scaling of global-mean radiative properties with surface temperature in the present day climate provides little useful guidance for estimates of the actual climate sensitivity to global changes.展开更多
Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigat...Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.展开更多
In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα(U) + ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a clas...In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα(U) + ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α(u). The resulting statistics are shown to have standard chi-squared or normal distributions asymptotically.Simulation studies are also constructed to illustrate the finite sample properties of the proposed statistics.展开更多
Missing data and time-dependent covariates often arise simultaneously in longitudinal studies,and directly applying classical approaches may result in a loss of efficiency and biased estimates.To deal with this proble...Missing data and time-dependent covariates often arise simultaneously in longitudinal studies,and directly applying classical approaches may result in a loss of efficiency and biased estimates.To deal with this problem,we propose weighted corrected estimating equations under the missing at random mechanism,followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present.Such procedure improves efficiency over generalized estimation equations approach with working independent assumption,via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption.The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries.We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter.The practical performance of our approach is demonstrated through numerical simulations and data analysis.展开更多
Joint roughness coefficient(JRC) is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS(joint wall compressive strength) model.Because JRC has such characteristics as nonuni...Joint roughness coefficient(JRC) is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS(joint wall compressive strength) model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.展开更多
The estimation of covariance matrices is central in array signal processing systems. This note addresses complex covariance estimation for the situation, where the complex data are available only as independent pairwi...The estimation of covariance matrices is central in array signal processing systems. This note addresses complex covariance estimation for the situation, where the complex data are available only as independent pairwise sets (observations) corresponding to individual elements of the matrix. The formulation for the empirical estimate and the normal maximum likelihood estimate is developed for the general case of different sample sizes for each observation. The approach allows, for example, the estimate of the p by p covariance matrix of a p-port sensor array from a two-port measurement instrument.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 40672186, 50809059)the Natural Science Foundation of Zhejiang Province (No. Y505008), China
文摘In order to study the reliability of the empirical estimation of joint shear strength by the JRC(joint roughness coefficient)-JCS(joint compressive strength) model,natural rock joints of dif-ferent lithologic characteristics and different sizes were selected as samples,and their shear strengths under dry and saturated conditions were measured by direct shear test and compared to those esti-mated by the JRC-JCS model.Comparison results show that for natural rock joints with joint surfaces closely matched,the average relative error of joint shear strength between empirical estimation and direct shear test is 9.9%;the reliability of the empirical estimation of joint shear strength by the JRC-JCS model is good under both dry and saturated conditions if the JRC is determined accounting for directional statistical measurements,scale effect and surface smoothing during shearing.However,for natural rock joints with joint surfaces mismatched,the average relative error of joint shear strength between empirical estimation and direct shear test is 39.9%;the reliability of empirical estimation of joint shear strength by the JRC-JCS model is questionable under both dry and saturated conditions.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘In this article,the empirical Bayes(EB)estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares(LS)estimator are investigated under mean square error matrix(MSEM)criterion.
文摘In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
文摘For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
文摘A control integration with the normal solar constant and one with it increased by 2.5% in the National Center for Atmospheric Research (NCAR) coupled atmosphere-ocean Climate System Model were conducted to see how well the actual realized global warming could be predicted just by analysis of the control results. This is a test, within a model context, of proposals that have been advanced to use knowledge of the present day climate to make "empirical" estimates of global climate sensitivity. The scaling of the top-of-the-atmosphere infrared flux and the planetary albedo as functions of surface temperature was inferred by examining four different temporal and geographical variations of the control simulations. Each of these inferences greatly overestimates the climate sensitivity of the model, largely because of the behavior of the cloud albedo. In each inference the control results suggest that cloudiness and albedo decrease with increasing surface temperature. However, the experiment with the increased solar constant actually has higher albedo and more cloudiness at most latitudes. The increased albedo is a strong negative feedback, and this helps account for the rather weak sensitivity of the climate in the NCAR model. To the extent that these model results apply to the real world, they suggest empirical evaluation of the scaling of global-mean radiative properties with surface temperature in the present day climate provides little useful guidance for estimates of the actual climate sensitivity to global changes.
基金supported by the Natural Science Foundation of China under Grant Nos.12031016,11061002,11801033,12071014 and 12131001the National Social Science Fund of China under Grant No.19ZDA121the Natural Science Foundation of Guangxi under Grant Nos.2015GXNSFAA139006 and LMEQF。
文摘Generalized linear models are usually adopted to model the discrete or nonnegative responses.In this paper,empirical likelihood inference for fixed design generalized linear models with longitudinal data is investigated.Under some mild conditions,the consistency and asymptotic normality of the maximum empirical likelihood estimator are established,and the asymptotic χ^(2) distribution of the empirical log-likelihood ratio is also obtained.Compared with the existing results,the new conditions are more weak and easy to verify.Some simulations are presented to illustrate these asymptotic properties.
基金supported in part by NSF of China(No.11461029)NSF of Jiangxi Province(No.20142BAB211014)YSFP of Jiangxi provincial education department(No.GJJ14350)
文摘In this paper, we consider the empirical likelihood-based inferences for varying coefficient models Y = X^τα(U) + ε when X are subject to missing at random. Based on the inverse probability-weighted idea, a class of empirical log-likelihood ratios, as well as two maximum empirical likelihood estimators, are developed for α(u). The resulting statistics are shown to have standard chi-squared or normal distributions asymptotically.Simulation studies are also constructed to illustrate the finite sample properties of the proposed statistics.
基金supported by the NNSF of China(No.11271347)the Fundamental Research Funds for the Central Universities
文摘Missing data and time-dependent covariates often arise simultaneously in longitudinal studies,and directly applying classical approaches may result in a loss of efficiency and biased estimates.To deal with this problem,we propose weighted corrected estimating equations under the missing at random mechanism,followed by developing a shrinkage empirical likelihood estimation approach for the parameters of interest when time-dependent covariates are present.Such procedure improves efficiency over generalized estimation equations approach with working independent assumption,via combining the independent estimating equations and the extracted additional information from the estimating equations that are excluded by the independence assumption.The contribution from the remaining estimating equations is weighted according to the likelihood of each equation being a consistent estimating equation and the information it carries.We show that the estimators are asymptotically normally distributed and the empirical likelihood ratio statistic and its profile counterpart follow central chi-square distributions asymptotically when evaluated at the true parameter.The practical performance of our approach is demonstrated through numerical simulations and data analysis.
基金supported by the National Natural Science Foundation of China (Nos. 40672186, 50809059)the Natural Science Foundation of Zhejiang Province (No.Y505008)
文摘Joint roughness coefficient(JRC) is the key parameter for the empirical estimation of joint shear strength by using the JRC-JCS(joint wall compressive strength) model.Because JRC has such characteristics as nonuniformity,anisotropy,and unhomogeneity,directional statistical measurement of JRC is the precondition for ensuring the reliability of the empirical estimation method.However,the directional statistical measurement of JRC is time-consuming.In order to present an ideal measurement method of JRC,new profilographs and roughness rulers were developed according to the properties of rock joint undulating shape based on the review of measurement methods of JRC.Operation methods of the profilographs and roughness rulers were also introduced.A case study shows that the instruments and operation methods produce an effective means for the statistical measurement of JRC.
文摘The estimation of covariance matrices is central in array signal processing systems. This note addresses complex covariance estimation for the situation, where the complex data are available only as independent pairwise sets (observations) corresponding to individual elements of the matrix. The formulation for the empirical estimate and the normal maximum likelihood estimate is developed for the general case of different sample sizes for each observation. The approach allows, for example, the estimate of the p by p covariance matrix of a p-port sensor array from a two-port measurement instrument.