The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-pr...The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.展开更多
Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squ...Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.展开更多
A new and convenient method is presented to calculate the total sensitivity indices defined by variance-based sensitivity analysis. By decomposing the output variance using error propagation equations, this method can...A new and convenient method is presented to calculate the total sensitivity indices defined by variance-based sensitivity analysis. By decomposing the output variance using error propagation equations, this method can transform the ＂double-loop＂ sampling procedure into ＂single-loop＂ one and obviously reduce the computation cost of analysis. In contrast with Sobors and Fourier amplitude sensitivity test （FAST） method, which is limited in non-correlated variables, the new approach is suitable for correlated input variables. An application in semiconductor assembling and test manufacturing （ATM） factory indicates that this approach has a good performance in additive model and simple non-additive model.展开更多
We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over...We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively,we show that the Brukner–Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained.These results provide an operational link between the previous interpretations of the Brukner–Zeilinger invariant information.展开更多
基金supported by the National Natural Science Foundation of China(No.41874001 and No.41664001)Support Program for Outstanding Youth Talents in Jiangxi Province(No.20162BCB23050)National Key Research and Development Program(No.2016YFB0501405)。
文摘The solution of the grey model(GM(1,1)model)generally involves equal-precision observations,and the(co)variance matrix is established from the prior information.However,the data are generally available with unequal-precision measurements in reality.To deal with the errors of all observations for GM(1,1)model with errors-in-variables(EIV)structure,we exploit the total least-squares(TLS)algorithm to estimate the parameters of GM(1,1)model in this paper.Ignoring that the effect of the improper prior stochastic model and the homologous observations may degrade the accuracy of parameter estimation,we further present a nonlinear total least-squares variance component estimation approach for GM(1,1)model,which resorts to the minimum norm quadratic unbiased estimation(MINQUE).The practical and simulative experiments indicate that the presented approach has significant merits in improving the predictive accuracy in comparison with control methods.
基金The research was supported by the National Natural Science Foundation of China(41204003)Scientific Research Foundation of ECIT(DHBK201113)Scientific Research Foundation of Jiangxi Province Key Laboratory for Digital Land(DLLJ201207)
文摘Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.
文摘A new and convenient method is presented to calculate the total sensitivity indices defined by variance-based sensitivity analysis. By decomposing the output variance using error propagation equations, this method can transform the ＂double-loop＂ sampling procedure into ＂single-loop＂ one and obviously reduce the computation cost of analysis. In contrast with Sobors and Fourier amplitude sensitivity test （FAST） method, which is limited in non-correlated variables, the new approach is suitable for correlated input variables. An application in semiconductor assembling and test manufacturing （ATM） factory indicates that this approach has a good performance in additive model and simple non-additive model.
基金supported by the National Natural Science Foundation of China under Grant Nos.11805143 and 11675113Beijing Municipal Commission of Education under Grant No.KZ201810028042。
文摘We investigate the total variance of a quantum state with respect to a complete set of mutually complementary measurements and its relation to the Brukner–Zeilinger invariant information.By summing the variances over any complete set of mutually unbiased measurements and general symmetric informationally complete measurements respectively,we show that the Brukner–Zeilinger invariant information associated with such types of quantum measurements is equal to the difference between the maximal variance and the total variance obtained.These results provide an operational link between the previous interpretations of the Brukner–Zeilinger invariant information.
