EFFICIENT ESTIMATION OF FUNCTIONAL-COEFFICIENT REGRESSION MODELS WITH DIFFERENT SMOOTHING VARIABLES

In this article,a procedure for estimating the coefficient functions on the functional-coefficient regression models with different smoothing variables in different coefficient functions is defined.First step,by the local linear technique and the averaged method,the initial estimates of the coefficient functions are given.Second step,based on the initial estimates,the efficient estimates of the coefficient functions are proposed by a one-step back-fitting procedure.The efficient estimators share the same asymptotic normalities as the local linear estimators for the functional-coefficient models with a single smoothing variable in different functions.Two simulated examples show that the procedure is effective.

Darboux Transformation and Soliton Solutions for a Variable-Coefficient Modified Kortweg-de Vries Model from Fluid Mechanics, Ocean Dynamics, and Plasma Mechanics

这份报纸是调查可变系数的修改 Kortweg-de Vries (vc-mKdV ) 为力学建模，它从液体力学，海洋动力学，和血浆描述一些状况。由 AblowitzKaupNewellSegur 过程和符号的计算， vc-MKdV 模型的宽松的对被导出。基于上述的宽松的对，然后， Darboux 转变被构造，一个新 one-soliton-like 答案也被获得。one-soliton-like 答案的特征被分析并且图形地讨论了在 solitonlike 繁殖说明可变系数的影响。

Various Methods for Constructing Auto-Bcklund Transformations for a Generalized Variable-Coefficient Korteweg-de Vries Model from Plasmas and Fluid Dynamics

<Abstract>In this paper,under the Painlevé-integrable condition,the auto-Bcklund transformations in different forms for a variable-coefficient Korteweg-de Vries model with physical interests are obtained through various methods including the Hirota method,truncated Painlevé expansion method,extended variable-coefficient balancing-act method,and Lax pair.Additionally,the compatibility for the truncated Painlevé expansion method and extended variable-coefficient balancing-act method is testified.

Unified Variable Selection for Varying Coefficient Models with Longitudinal Data

Variable selection for varying coefficient models includes the separation of varying and constant effects,and the selection of variables with nonzero varying effects and those with nonzero constant effects.This paper proposes a unified variable selection approach called the double-penalized quadratic inference functions method for varying coefficient models of longitudinal data.The proposed method can not only separate varying coefficients and constant coefficients,but also estimate and select the nonzero varying coefficients and nonzero constant coefficients.It is suitable for variable selection of linear models,varying coefficient models,and partial linear varying coefficient models.Under regularity conditions,the proposed method is consistent in both separation and selection of varying coefficients and constant coefficients.The obtained estimators of varying coefficients possess the optimal convergence rate of non-parametric function estimation,and the estimators of nonzero constant coefficients are consistent and asymptotically normal.Finally,the authors investigate the finite sample performance of the proposed method through simulation studies and a real data analysis.The results show that the proposed method performs better than the existing competitor.

计及弱磁效应的直驱式波浪发电系统变系数模型预测控制策略

为提高波浪发电系统(wave energy converter,WEC)能量捕获效率,并保证其在运行过程中满足系统的各种约束条件,该文以平均捕获功率最优为目标,提出计及弱磁效应的直驱式波浪发电系统变系数模型预测控制(model predictive control,MPC)策略。针对波浪激励力过大导致的变流器输出电压过调制问题,将弱磁控制引入优化算法,在满足发电机弱磁极限的前提下增大发电系统的运行范围,提高WEC的能量捕获效率。此外,基于仿真分析,发现了规则波下MPC目标函数的正则系数与平均捕获功率的对应关系。在此基础上,引入快速傅里叶变换(fast Fourier transformation,FFT)与叠加定理,构建了适用于不规则波输入的直驱式WEC变系数MPC控制策略。仿真结果表明,在不规则波浪下,所提方案能在满足系统约束条件的同时,有效提高能量捕获效率。

Variable Selection for Fixed Effects Varying Coefficient Models

We consider the problem of variable selection for the fixed effects varying coefficient models. A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.

Instrumental Variable Type Estimation for Generalized Varying Coefficient Models with Error-Prone Covariates

In this paper,the estimation for a class of generalized varying coefficient models with error-prone covariates is considered.By combining basis function approximations with some auxiliary variables,an instrumental variable type estimation procedure is proposed.The asymptotic results of the estimator,such as the consistency and the weak convergence rate,are obtained.The proposed procedure can attenuate the effect of measurement errors and have proved workable for finite samples.

Model Detection and Variable Selection for Varying Coefficient Models with Longitudinal Data

In this puper, we consider the problem of variabie selection and model detection in varying coefficient models with longitudinM data. We propose a combined penalization procedure to select the significant variables, detect the true structure of the model and estimate the unknown regression coefficients simultaneously. With appropriate selection of the tuning parameters, we show that the proposed procedure is consistent in both variable selection and the separation of varying and constant coefficients, and the penalized estimators have the oracle property. Finite sample performances of the proposed method are illustrated by some simulation studies and the real data analysis.

Variable Selection for Semiparametric Varying-Coefficient Partially Linear Models with Missing Response at Random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.

Semiparametric estimation of average treatment effect through a random coefficient dummy endogenous variable model

This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations:an outcome equation and a decision equation.Given the linear restriction in outcome and decision equations,Chen(1999) provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen's estimator by relaxing the linear index into a nonparametric function,which greatly reduces the risk of model misspecification. A two-step approach is proposed:the first step uses a nonparametric regression estimator for the decision variable,and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore,we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.

Variable selection for single-index varying-coefficient model

We consider the problem of variable selection for single-index varying-coefficient model, and present a regularized variable selection procedure by combining basis function approximations with SCAD penalty. The proposed procedure simultaneously selects significant covariates with functional coefficients and local significant variables with parametric coefficients. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. The proposed method can naturally be applied to deal with pure single-index model and varying-coefficient model. Finite sample performances of the proposed method are illustrated by a simulation study and the real data analysis.

Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

Variable Selection for Varying-Coefficient Models with Missing Response at Random

In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.

基于变差分系数的变网格弹性波全波形反演

全波形反演充分利用地震波传播的振幅、相位和旅行时等信息,相较于旅行时层析能够获得分辨率和精度更高的反演结果。当浅层介质速度较低时,为了保证正演模拟精度,通常需要使用较细的网格对低速层进行采样。然而,对整个模型用细网格剖分会导致巨大的计算量以及存储量,同时模型的高速区域也会产生过采样现象,这些问题会在全波形反演过程中被进一步放大。为了避免这些问题,引入了一种基于变差分系数的变网格弹性波动方程有限差分正演模拟方法。首先,基于Taylor展开式推导了变网格波场模拟的差分系数,实现了变网格波场模拟;其次,将变差分系数正演模拟方法应用于全波形反演中的正演模拟、残差反传和波场重构中,实现了基于变差分系数的变网格弹性波全波形反演。在全波形反演时,分别采用多尺度反演策略和常规的共轭梯度法迭代求解。使用细网格剖分速度较低的浅部低速层和粗网格剖分速度较高的中深层,既可以保证浅层的反演精度,又可以避免中深层的过采样。模型数据反演结果表明,基于变差分系数的变网格全波形反演相较于均匀粗网格全波形反演可以更有效实现低速异常体的准确刻画。含噪数据测试表明,提出的全波形反演方法具有较强的抗噪性。

融合新旧产品退化信息的可靠性建模研究

针对2阶段退化产品截尾数据难以进行精确可靠性评估问题,利用贝叶斯融合新产品截尾数据和相似产品2阶段退化数据信息,并采用变系数分段回归模型和变点思想建立了变系数分段退化可靠性评估模型。首先,运用泰勒展开式和遗传算法得到相似产品回归模型的参数估计值并拟合分布。其次,通过贝叶斯方法融合新旧产品第1阶段退化数据信息,基于变点的连续性建立阶段关系式得到第2阶段新产品参数估计量期望和方差。最后,利用相似产品退化量的分布类型和矩估计方法得到新产品退化量的分布以及分段可靠度函数。算例分析结果验证了该模型的有效性和精准性。

变系数模型的稳健变量选择与结构识别

研究了稳健回归下变系数模型的变量选择和模型结构识别问题。利用B样条基函数近似非参数系数函数,建立自适应组Lasso双惩罚函数选择变系数模型中的重要变量并且识别具有常数效应的协变量,同时估计未知的非参数系数函数。在一定条件下,证明了所提出的惩罚估计量具有相合性和稀疏性。通过数值模拟验证所提方法的有限样本性质。

成渝城市群PM_(2.5)影响因素的半变系数模型分析

随着西南地区成为我国经济高质量发展新高地,成渝城市群的可持续发展受到各界关注。利用半变系数面板数据模型,以成渝城市群为研究对象,探讨PM_(2.5)与气温、降水量、气压、平均风速、相对湿度之间的动态关系。首先,通过散点图和拟合回归曲线分析不同气象因素与PM_(2.5)之间的线性关系、非线性关系,以及气象因素间的相互作用。其次,将半参数固定效应估计量、半参数随机效应估计量与测试程序相结合,区分固定效应和随机效应。研究发现:不可观测的个体效应为固定效应;气温对PM_(2.5)具有负向线性影响;气压、平均风速、降水量和相对湿度对PM_(2.5)具有复杂的非线性影响;气压分别与平均风速、降水量和相对湿度共同作用于PM_(2.5)。建议成渝城市群充分利用地理区位特征植树造林,调整能源结构,进行人工降雨,运用科技手段治理PM_(2.5),以此减少空气污染。

部分线性变系数模型的贝叶斯分位数回归

针对部分线性变系数模型的参数估计问题,采用B样条方法逼近非参数部分的未知光滑函数,进而利用非对称拉普拉斯分布实现贝叶斯分位数回归,并基于Gibbs抽样推导出所有未知参数的后验分布,通过数值模拟比较分析了贝叶斯分位数回归与分位数回归参数估计的优劣,结果表明,在均方误差准则下,贝叶斯分位数回归的估计效果更优。最后,通过实例分析说明了所提方法的有效性。

简支工字形钢混组合梁横向分布系数研究及简化计算

钢混组合梁兼具钢材的抗拉性能及混凝土的抗压性能,整体造价较钢梁有明显优势,在城市建设中具有明显的运用优势。然而,基于工程实例对钢混组合梁开展横向分布系数的研究和简化计算较为匮乏。因此,选取一项桥梁改造工程,以简支工字形钢混组合梁为对象,通过建立全桥梁格有限元模型分析桥宽、中间横梁间距、中间横梁强度、主梁片数等参数,研究简支工字形钢混组合梁横向分布系数。将其结果与刚性横梁法、刚接板梁法、比拟正交异性板梁法相比,简化了简支工字形钢混组合梁有限元计算。

基于灰色关联分析法的物联网数据异常检测方法

物联网数据具有构成复杂、规模庞大、异常形式多样化的特征,导致基于传统异常检测方法得到的结果正确率偏低。文中提出了一种基于灰色关联分析法的物联网数据异常检测方法。该方法利用灰色关联模型计算得到灰色关联系数,对原始物联网数据中的自有变量相关性进行排序,随后采用前向选择法进行变量排序选择,确定反推得到的特征参数误差达到最小值时的变量,并将其作为最优变量子集;在异常检测阶段,用最优变量子集对物联网数据进行异常位置寻优,实现异常检测。测试结果表明,该方法在不同攻击下,异常数据检测结果的F1值未出现明显的波动,对应的F1值为0.84~0.90。