1 Theorems Consider the following nonlinear autoregressive modelx<sub>t</sub>=φx<sub>t-1</sub>+ε<sub>t</sub>h(x<sub>t-1</sub>θ) （1）with the assumptions:（A1）│φ│...1 Theorems Consider the following nonlinear autoregressive modelx<sub>t</sub>=φx<sub>t-1</sub>+ε<sub>t</sub>h(x<sub>t-1</sub>θ) （1）with the assumptions:（A1）│φ│【1,θ=（θ<sub>0</sub>,θ<sub>1</sub>）∈ is an open set in R<sup>2</sup>,（A2） {ε<sub>t</sub>} is a sequenee of independent identically distributed random variables suchthatEε<sub>t</sub>=0, Eε<sub>t</sub><sup>2</sup>=1, E│ε<sub>t</sub>│<sup>4+δ</sup>【∞,for some δ】0, （2）and ε<sub>t</sub> is independent of x<sub>t-1</sub>, （A3） h（·） is an everywhere positive measurable function satisfying that as│x │→∞,h（x）→∞, h（x）/│x│→0, and for each C】0, sup h（x）【∞,展开更多
In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least ...In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.展开更多
In this paper,a nonparametric multivariate regression model with long memory covariates and long memory errors is considered.We approximate the nonparametric multivariate regression function by the weighted additive o...In this paper,a nonparametric multivariate regression model with long memory covariates and long memory errors is considered.We approximate the nonparametric multivariate regression function by the weighted additive one-dimensional functions.The local linear smoothing and least squares method are proposed for the one-dimensional regression estimation and the weight parameters estimation,respectively.The asymptotic behaviors of the proposed estimators are investigated.展开更多
目的探讨昼夜温差(diurnal temperature range,DTR)影响慢性肾脏病(chronic kidney diseases,CKD)日住院人次的影响。方法收集2019年1月1日至2020年12月31日乌鲁木齐市4所三甲医院、4所二甲医院、1所一甲医院CKD日住院人次数据,同期气...目的探讨昼夜温差(diurnal temperature range,DTR)影响慢性肾脏病(chronic kidney diseases,CKD)日住院人次的影响。方法收集2019年1月1日至2020年12月31日乌鲁木齐市4所三甲医院、4所二甲医院、1所一甲医院CKD日住院人次数据,同期气象及污染物数据来自于乌鲁木齐市主城区的6个国控监测点,采用分布滞后非线性模型,控制星期几效应、假期效应、长期时间趋势及其它因素,分析DTR与CKD日住院人次的关系。结果CKD日住院人次与DTR(滞后0~21 d)的暴露-反应曲线呈“N”形,CKD患者住院风险随DTR的升高呈先上升后下降趋势。低度和高度DTR对CKD患者住院的影响存在一定的滞后效应,中度DTR对住院影响较小;DTR=5℃时,单日效应出现在第3天[RR=1.081,95%CI(1.020,1.145),P<0.05],最大效应出现在第21天[RR=1.090,95%CI(1.014,1.173),P<0.05];高度DTR=14℃(P_(95))时,单日效应出现在第4天[RR=1.086,95%CI(1.007,1.172),P<0.05],最大效应出现在第5天[RR=1.089,95%CI(1.009,1.176),P<0.05],累积滞后均暂未发现有统计学差异。男性和年龄<65岁的CKD患者更易受到DTR的影响,寒冷季节和四季更替时DTR变化对CKD患者住院的影响更大。结论男性与<65岁CKD患者更易受到DTR的影响,在寒冷季节和四季交替DTR变化时更应重点保护易感人群免受DTR的影响。展开更多
时间序列插补旨在根据现有数据填补缺失值以恢复数据的完整性.目前基于RNN的插补方法存在较大的误差,并且增加网络层数容易出现梯度爆炸和消失问题,而基于GAN和VAE的插补方法经常面临训练困难和模式崩溃的挑战.为解决上述问题,本文提出...时间序列插补旨在根据现有数据填补缺失值以恢复数据的完整性.目前基于RNN的插补方法存在较大的误差,并且增加网络层数容易出现梯度爆炸和消失问题,而基于GAN和VAE的插补方法经常面临训练困难和模式崩溃的挑战.为解决上述问题,本文提出了一种基于扩散与时频注意力的时间序列插补模型DTFA (diffusion model and time-frequency attention),通过反向扩散实现从高斯噪声中重建缺失数据.具体而言,本研究利用多尺度卷积模块与二维注意力机制捕获时域数据中的时间依赖性,并利用MLP与二维注意力机制学习频域数据的实部与虚部信息.此外,本研究通过线性插补模块以对现有的观测数据进行初步的数据增强,从而更好地指导模型的插补过程.最后,本研究通过最小化真实噪声与估计噪声的欧氏距离来训练噪声估计网络,并利用反向扩散实现对时序数据的缺失插补.本研究的实验结果表明, DTFA在ETTm1、WindPower和Electricity这3个公开数据集上的插补效果均优于近年主流的基线模型.展开更多
基金Project supported by the National Natural Science Foundation of China and Probability Laboratory, Institute of Applied Mathematics, Chinese Academy of Sciences.
文摘1 Theorems Consider the following nonlinear autoregressive modelx<sub>t</sub>=φx<sub>t-1</sub>+ε<sub>t</sub>h(x<sub>t-1</sub>θ) （1）with the assumptions:（A1）│φ│【1,θ=（θ<sub>0</sub>,θ<sub>1</sub>）∈ is an open set in R<sup>2</sup>,（A2） {ε<sub>t</sub>} is a sequenee of independent identically distributed random variables suchthatEε<sub>t</sub>=0, Eε<sub>t</sub><sup>2</sup>=1, E│ε<sub>t</sub>│<sup>4+δ</sup>【∞,for some δ】0, （2）and ε<sub>t</sub> is independent of x<sub>t-1</sub>, （A3） h（·） is an everywhere positive measurable function satisfying that as│x │→∞,h（x）→∞, h（x）/│x│→0, and for each C】0, sup h（x）【∞,
基金Supported by the Educational Commission of Hubei Province of China(Grant No.D20112503)National Natural Science Foundation of China(Grant Nos.11071022,11231010 and 11028103)the foundation of Beijing Center of Mathematics and Information Sciences
文摘In this paper, the parameters of a p-dimensional linear structural EV(error-in-variable)model are estimated when the coefficients vary with a real variable and the model error is time series.The adjust weighted least squares(AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.
基金Supported by the National Natural Science Foundation of China(No.11671194 and No.11501287)
文摘In this paper,a nonparametric multivariate regression model with long memory covariates and long memory errors is considered.We approximate the nonparametric multivariate regression function by the weighted additive one-dimensional functions.The local linear smoothing and least squares method are proposed for the one-dimensional regression estimation and the weight parameters estimation,respectively.The asymptotic behaviors of the proposed estimators are investigated.
文摘时间序列插补旨在根据现有数据填补缺失值以恢复数据的完整性.目前基于RNN的插补方法存在较大的误差,并且增加网络层数容易出现梯度爆炸和消失问题,而基于GAN和VAE的插补方法经常面临训练困难和模式崩溃的挑战.为解决上述问题,本文提出了一种基于扩散与时频注意力的时间序列插补模型DTFA (diffusion model and time-frequency attention),通过反向扩散实现从高斯噪声中重建缺失数据.具体而言,本研究利用多尺度卷积模块与二维注意力机制捕获时域数据中的时间依赖性,并利用MLP与二维注意力机制学习频域数据的实部与虚部信息.此外,本研究通过线性插补模块以对现有的观测数据进行初步的数据增强,从而更好地指导模型的插补过程.最后,本研究通过最小化真实噪声与估计噪声的欧氏距离来训练噪声估计网络,并利用反向扩散实现对时序数据的缺失插补.本研究的实验结果表明, DTFA在ETTm1、WindPower和Electricity这3个公开数据集上的插补效果均优于近年主流的基线模型.
