In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new...Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.展开更多
For practical engineering structures,it is usually difficult to measure external load distribution in a direct manner,which makes inverse load identification important.Specifically,load identification is a typical inv...For practical engineering structures,it is usually difficult to measure external load distribution in a direct manner,which makes inverse load identification important.Specifically,load identification is a typical inverse problem,for which the models(e.g.,response matrix)are often ill-posed,resulting in degraded accuracy and impaired noise immunity of load identification.This study aims at identifying external loads in a stiffened plate structure,through comparing the effectiveness of different methods for parameter selection in regulation problems,including the Generalized Cross Validation(GCV)method,the Ordinary Cross Validation method and the truncated singular value decomposition method.With demonstrated high accuracy,the GCV method is used to identify concentrated loads in three different directions(e.g.,vertical,lateral and longitudinal)exerted on a stiffened plate.The results show that the GCV method is able to effectively identify multi-source static loads,with relative errors less than 5%.Moreover,under the situation of swept frequency excitation,when the excitation frequency is near the natural frequency of the structure,the GCV method can achieve much higher accuracy compared with direct inversion.At other excitation frequencies,the average recognition error of the GCV method load identification less than 10%.展开更多
Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector corr...Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D- + H2 and H- + D2 is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ) (dσ00/dωt), (2π/σ) (dσ20/dσ20), (27π/σ) (dσ22+/dwt), and (2π/σ)(dπ/σ) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θr), P(~r) and P(Oφ) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j^1 sensitively depend on reagent molecule vibration.展开更多
Quasi-classical trajectory (QCT) studies on the stereodynamics of H + BrO → O+ HBr reaction have been performed on the X1A' state of ab initio potential energy surface by Peterson [Peterson K A 2000 J. Chem. Phy...Quasi-classical trajectory (QCT) studies on the stereodynamics of H + BrO → O+ HBr reaction have been performed on the X1A' state of ab initio potential energy surface by Peterson [Peterson K A 2000 J. Chem. Phys. 113 4598] in a collision energy range from 0 kcal/mol to 6 kcal/mol. Two of the polarization-dependent generalized differential cross sections (PDDCSs), (2π/σ)(dσ 00/d ω) (PDDCSoo) and (2π/σ)(dσ20/doh) (PDDCS20) are considered. The rotational polarizations of these products show sensitive behaviors to the calculated collision energy range. Furthermore, in order to gain more knowledge about vector correlations, the product angular distribution, P(θr), and the dihedral angle, P (Фr), are calculated, and the results indicate that both the rotational alignment and orientation of the product are enhanced as collision energy increases.展开更多
In this paper, the stereodynamics of Li + DF → Li F + D reaction is investigated by the quasi-classical trajectory(QCT)method on the ^2A' potential energy surface(PES) at a relatively low collision energy of 8...In this paper, the stereodynamics of Li + DF → Li F + D reaction is investigated by the quasi-classical trajectory(QCT)method on the ^2A' potential energy surface(PES) at a relatively low collision energy of 8.76 kcal/mol. The scalar properties of the title reaction such as reaction probability and cross section are studied with vibrational quantum number of v = 1–6. The product angular distributions P(θr) and P(φr) are presented in the same vibrational level range. Moreover, two polarization-dependent generalized differential cross sections(PDDCSs), i.e., the PDDCS00 and PDDCS22+are calculated as well. These stereodynamical results demonstrate sensitive behaviors to the vibrational quantum numbers.展开更多
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
基金by National Key R&D Program of China(2020AAA0105200)the Ministry of Science and Technology of China(Grant no.2016YFB0502301)+1 种基金the National Natural Science Foundation of China(Grant nos.11871294,12031016,11971323,71925007,72042019,72091212 and 12001559)a joint grant from the Academy for Multidisciplinary Studies,Capital Normal University.
文摘Frequentist model averaging has received much attention from econometricians and statisticians in recent years.A key problem with frequentist model average estimators is the choice of weights.This paper develops a new approach of choosing weights based on an approximation of generalized cross validation.The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors.Especially,the optimality is built under both discrete and continuous weigh sets.Compared with the existing approach based on Mallows criterion,the conditions required for the asymptotic optimality of the proposed method are more reasonable.Simulation studies and real data application show good performance of the proposed estimators.
基金funding for this study from National Key R&D Program of China(2018YFA0702800)National Natural Science Foundation of China(12072056)+1 种基金the Fundamental Research Funds for the Central Universities(DUT19LK49)Nantong Science and Technology Plan Project(No.MS22019016).
文摘For practical engineering structures,it is usually difficult to measure external load distribution in a direct manner,which makes inverse load identification important.Specifically,load identification is a typical inverse problem,for which the models(e.g.,response matrix)are often ill-posed,resulting in degraded accuracy and impaired noise immunity of load identification.This study aims at identifying external loads in a stiffened plate structure,through comparing the effectiveness of different methods for parameter selection in regulation problems,including the Generalized Cross Validation(GCV)method,the Ordinary Cross Validation method and the truncated singular value decomposition method.With demonstrated high accuracy,the GCV method is used to identify concentrated loads in three different directions(e.g.,vertical,lateral and longitudinal)exerted on a stiffened plate.The results show that the GCV method is able to effectively identify multi-source static loads,with relative errors less than 5%.Moreover,under the situation of swept frequency excitation,when the excitation frequency is near the natural frequency of the structure,the GCV method can achieve much higher accuracy compared with direct inversion.At other excitation frequencies,the average recognition error of the GCV method load identification less than 10%.
基金supported by the National Natural Science Foundation of China (Grant No.11074103)the Discipline ConstructionFund of Ludong University,China
文摘Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J. Chem. Phys. 121 9343], the effect of the reagent vibration on vector correlation of the ion-molecule reactions D- + H2 and H- + D2 is studied at a collision energy of 35.7 kcal/mol. Four generalized polarization-dependent differential cross sections (2π/σ) (dσ00/dωt), (2π/σ) (dσ20/dσ20), (27π/σ) (dσ22+/dwt), and (2π/σ)(dπ/σ) are presented in the centre-of-mass reference frame, separately. At the same time, the effects on the product angular distributions P(θr), P(~r) and P(Oφ) of the title reactions are also analysed. The calculated results show that the scattering tendencies of the product HD, the alignment and the orientation of j^1 sensitively depend on reagent molecule vibration.
基金Project supported by the Science Fund from Jilin University,China(Grant No.419080106440)the Chinese National Fusion Project for ITER(Grant No.2010GB104003)the National Natural Science Foundation of China(Grant No.10974069)
文摘Quasi-classical trajectory (QCT) studies on the stereodynamics of H + BrO → O+ HBr reaction have been performed on the X1A' state of ab initio potential energy surface by Peterson [Peterson K A 2000 J. Chem. Phys. 113 4598] in a collision energy range from 0 kcal/mol to 6 kcal/mol. Two of the polarization-dependent generalized differential cross sections (PDDCSs), (2π/σ)(dσ 00/d ω) (PDDCSoo) and (2π/σ)(dσ20/doh) (PDDCS20) are considered. The rotational polarizations of these products show sensitive behaviors to the calculated collision energy range. Furthermore, in order to gain more knowledge about vector correlations, the product angular distribution, P(θr), and the dihedral angle, P (Фr), are calculated, and the results indicate that both the rotational alignment and orientation of the product are enhanced as collision energy increases.
基金Project supported by the Fund from the Jilin University,China(Grant No.419080106440)the Chinese National Fusion Project for the International Thermonuclear Experimental Reactor(ITER)(Grant No.2010GB104003)the National Natural Science Foundation of China(Grant No.10974069)
文摘In this paper, the stereodynamics of Li + DF → Li F + D reaction is investigated by the quasi-classical trajectory(QCT)method on the ^2A' potential energy surface(PES) at a relatively low collision energy of 8.76 kcal/mol. The scalar properties of the title reaction such as reaction probability and cross section are studied with vibrational quantum number of v = 1–6. The product angular distributions P(θr) and P(φr) are presented in the same vibrational level range. Moreover, two polarization-dependent generalized differential cross sections(PDDCSs), i.e., the PDDCS00 and PDDCS22+are calculated as well. These stereodynamical results demonstrate sensitive behaviors to the vibrational quantum numbers.