Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of e...Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.展开更多
A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the ...A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the objective function and constraint function are M-derivative,under the assumption of near conesubconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem.Under the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.展开更多
In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficienc...In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficiency andε-strict efficiency and has many desirable properties.We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional.Moreover,some examples are given to illustrate the main conclusions.展开更多
文摘Once invertibility for a causal TARMA series is defined and accompanied by conditions on the probability parameters of the model, all focus concentrates on the maximum likelihood estimators. Under the coexistence of essential causality and invertibility, the estimators are shown to be convergent to the real values and asymptotically obedient to the Gaussian distribution: their variance matrix identifies with a classic result. Some real-like examples are simulated and simplification attempts include the derivation of the non-parametric chi-square test extension for stationary TAR series.
基金This research was supported by the National Natural Science Foundation of China Grant(11961047)the Natural Science Foundation of Jiangxi Province(20192BAB201010).
文摘A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the objective function and constraint function are M-derivative,under the assumption of near conesubconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem.Under the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.
基金This research was supported by the National Natural Science Foundation of China(No.11671062)the Chongqing Municipal Education Commission(No.KJ1500310)the Doctor startup fund of Chongqing Normal University(No.16XLB010).
文摘In this paper,we propose a kind of unified strict efficiency named E-strict efficiency via improvement sets for vector optimization.This kind of efficiency is shown to be an extension of the classical strict efficiency andε-strict efficiency and has many desirable properties.We also discuss some relationships with other properly efficiency based on improvement sets and establish the corresponding scalarization theorems by a base-functional and a nonlinear functional.Moreover,some examples are given to illustrate the main conclusions.
