In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asy...In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.展开更多
Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed ...Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-展开更多
In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction...In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.展开更多
为完善拱形明洞结构可靠性设计方法,利用模型试验、数值模拟及理论分析等,结合现场实际,开展了落石冲击下无回填土拱形明洞破坏特征及失效模式、极限承载力、落石冲击荷载及极限状态表达式等的研究.首先,根据落石冲击下无回填土拱形明...为完善拱形明洞结构可靠性设计方法,利用模型试验、数值模拟及理论分析等,结合现场实际,开展了落石冲击下无回填土拱形明洞破坏特征及失效模式、极限承载力、落石冲击荷载及极限状态表达式等的研究.首先,根据落石冲击下无回填土拱形明洞结构失效破坏特征,将结构局部失效范围部分简化为四边固支方形钢筋混凝土板结构,利用塑性极限原理按刚塑性板进行准静态极限荷载计算,得到结构极限承载力即抗力;其次,将离散元颗粒流数值模拟方法得到的落石冲击力最大峰值作为钢筋混凝土板顶部落石冲击力,通过回归分析,得到用落石重力势能的幂函数表示的落石冲击荷载表达式;再次,将得到的结构抗力与落石冲击荷载联立得到极限状态方程,利用MABLAB软件编程求得结构可靠指标,通过与目标可靠指标的比较,进行结构可靠度设计与优化;最后,利用所建立的结构可靠度设计方法,对某客专双线拱形明洞设计进行了可靠度检算.研究结果表明:当落石高度为5~15 m、落石重量为1~2 k N时,原设计明洞结构可靠指标可达到4.2;当将原设计的C35混凝土调整为C40,钢筋由HRB335调整为HRB500后,落石高度为5~20 m、落石重量为1~2 k N范围时的结构可靠指标可达到5.4以上.展开更多
文摘In this paper, the estimation of the parameters in partial functional linear models with ARCH(p) errors is discussed. With employing the functional principle component, a hybrid estimating method is suggested. The asymptotic normality of the proposed estimators for both the linear parameter in the mean model and the parameter in the ARCH error model is obtained, and the convergence rate of the slope function estimate is established. Besides, some simulations and a real data analysis are conducted for illustration, and it is shown that the proposed method performs well with a finite sample.
文摘Suppose that the time series Xt satisfieswhere α0≥δ＞0,αi≥0 for i=1,2,…,q;βi,i=1,…,p, are real numbers; p and q are the order of the model. The sequence {ξt};（0,1） and is independent of {hs,s≤t} for fixed t. The above model is usually written as AR（p）-ARCH（q）.We consider stationary series AR（p）-ARCH（q） model and assume the stationary field is θ0. We express this statement asH1:α1≥α2…≥αq,β1≥β2≥…≥βp and we consider an order restricted testing problem, which is to testH0:α1=α2=…=αq,β1=β2=…=βpagainst H1-H0. We derive the likelihood ratio （LR） test statistic and its asymptotic distri-
文摘In this paper, we study a stationary AR（p）-ARCH（q） model with parameter vectors α and β. We propose a method for computing the maximum likelihood estimator （MLE） of parameters under the nonnegative restriction. A similar method is also proposed for the case that the parameters are restricted by a simple order： α1≥α2≥…≥αq and β1≥β2≥…≥βp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio （LR） test statistic for the testing problem and derive its asymptotic null distribution.
文摘为完善拱形明洞结构可靠性设计方法,利用模型试验、数值模拟及理论分析等,结合现场实际,开展了落石冲击下无回填土拱形明洞破坏特征及失效模式、极限承载力、落石冲击荷载及极限状态表达式等的研究.首先,根据落石冲击下无回填土拱形明洞结构失效破坏特征,将结构局部失效范围部分简化为四边固支方形钢筋混凝土板结构,利用塑性极限原理按刚塑性板进行准静态极限荷载计算,得到结构极限承载力即抗力;其次,将离散元颗粒流数值模拟方法得到的落石冲击力最大峰值作为钢筋混凝土板顶部落石冲击力,通过回归分析,得到用落石重力势能的幂函数表示的落石冲击荷载表达式;再次,将得到的结构抗力与落石冲击荷载联立得到极限状态方程,利用MABLAB软件编程求得结构可靠指标,通过与目标可靠指标的比较,进行结构可靠度设计与优化;最后,利用所建立的结构可靠度设计方法,对某客专双线拱形明洞设计进行了可靠度检算.研究结果表明:当落石高度为5~15 m、落石重量为1~2 k N时,原设计明洞结构可靠指标可达到4.2;当将原设计的C35混凝土调整为C40,钢筋由HRB335调整为HRB500后,落石高度为5~20 m、落石重量为1~2 k N范围时的结构可靠指标可达到5.4以上.
