The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal...The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal component analysis using this method.Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established.We also provide the convergence rate of the variance estimation of the measurement error.Based on the results,the number of observations within each curve can be of any rate relative to the sample size,which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.展开更多
通过调查京沪高速公路沂淮江段动态称重系统的交通轴载数据,研究了该路段交通荷载参数、货车的超载情况以及交通轴载谱。根据分析结果提出了以单轴双轮120 k N作为高速公路重载交通沥青路面的设计轴载、轮胎接地压强0.85 MPa为设计荷载...通过调查京沪高速公路沂淮江段动态称重系统的交通轴载数据,研究了该路段交通荷载参数、货车的超载情况以及交通轴载谱。根据分析结果提出了以单轴双轮120 k N作为高速公路重载交通沥青路面的设计轴载、轮胎接地压强0.85 MPa为设计荷载;发现用正态分布模型表征该路段单轴双轮轴载谱(R^2=0.95),能够比较真实地反映该路段的荷载特性,提出以该模型作为随机荷载的加载方案;并使用简化的荷载分布作为室内试验进行变幅荷载的加载方案。展开更多
基金supported by National Natural Science Foundation of China(project number:11771146,11831008,81530086,11771145)the National Social Science Foundation Key Program(17ZDA091)+2 种基金the 111 Project(B14019)Programof Shanghai Subject Chief Scientist(14XD1401600)supported by the China Postdoctoral Science Foundation(2018M630393).
文摘The unified weighing scheme for the local-linear smoother in analysing functional data can deal with data that are dense,sparse or of neither type.In this paper,we focus on the convergence rate of functional principal component analysis using this method.Almost sure asymptotic consistency and rates of convergence for the estimators of eigenvalues and eigenfunctions have been established.We also provide the convergence rate of the variance estimation of the measurement error.Based on the results,the number of observations within each curve can be of any rate relative to the sample size,which is consistent with the earlier conclusions about the asymptotic properties of the mean and covariance estimators.
文摘通过调查京沪高速公路沂淮江段动态称重系统的交通轴载数据,研究了该路段交通荷载参数、货车的超载情况以及交通轴载谱。根据分析结果提出了以单轴双轮120 k N作为高速公路重载交通沥青路面的设计轴载、轮胎接地压强0.85 MPa为设计荷载;发现用正态分布模型表征该路段单轴双轮轴载谱(R^2=0.95),能够比较真实地反映该路段的荷载特性,提出以该模型作为随机荷载的加载方案;并使用简化的荷载分布作为室内试验进行变幅荷载的加载方案。
