In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to...In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .展开更多
Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a k...Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.展开更多
A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presen...A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.展开更多
This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early w...Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.展开更多
Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionall...Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.展开更多
在航迹随机有限集的分布式多目标跟踪方法中,同一目标在不同传感器下估计航迹可能出现起始时间或航迹长度不一致的问题,提出一种基于航迹状态空间结构(state space structure,SSS)的分布式跟踪方法以及该方法的高斯混合模型实现。在基...在航迹随机有限集的分布式多目标跟踪方法中,同一目标在不同传感器下估计航迹可能出现起始时间或航迹长度不一致的问题,提出一种基于航迹状态空间结构(state space structure,SSS)的分布式跟踪方法以及该方法的高斯混合模型实现。在基于加权算术平均融合准则的分布式多目标跟踪框架下,结合航迹概率假设密度滤波器与航迹基数概率假设密度滤波器,利用航迹SSS信息,将航迹随机有限集的信息融合问题分治为多个独立的单一线性空间内子随机有限集信息融合问题。仿真实验基于广义最优子模式匹配度量方法比较了该方法与多种跟踪方法的跟踪性能,该方法估计结果与真实航迹误差最小,表明了该方法的有效性。展开更多
制造业集聚是城市发展的重要动力,同时也可能对生态环境产生负效应。论文拟以无锡市区为例,利用核密度函数(Kernel Density Distribution)对污染密集型制造业集聚程度进行评价,按照河流自然综合特征划分的环境单元进行污染物分布格局评...制造业集聚是城市发展的重要动力,同时也可能对生态环境产生负效应。论文拟以无锡市区为例,利用核密度函数(Kernel Density Distribution)对污染密集型制造业集聚程度进行评价,按照河流自然综合特征划分的环境单元进行污染物分布格局评价,在此基础上构建污染企业分布密度—COD排放量的双变量空间自相关模型,探讨制造业与河道污染物分布格局的定量关系,揭示制造业集聚和水污染的空间关联性。模型分析表明:无锡市区的污染密集型制造业呈现向郊区和环境非敏感区集聚的趋势,污染强度以主要运河为轴线向两翼地区逐渐衰减,二者空间格局的关联性存在行业差异性,污染物分布与纺织、石油化工业以及冶金业集聚和扩散格局的空间关联性较为显著,而与食品制造业和造纸印刷业的空间关联性则不显著。论文进一步根据产业集聚与污染格局的空间关联模式,将研究区域划分为高集聚—高污染、低集聚—低污染、低集聚—高污染、高集聚—低污染四种类型区,并提出相应的产业准入导向。本研究从空间效应角度为产业集聚与生态环境之间关联机理探讨提供新的视角,也可以作为制造业布局调整的科学依据。展开更多
基金Supported by Natural Science Foundation of Beijing City and National Natural Science Foundation ofChina(2 2 30 4 1 0 0 1 30 1
文摘In this paper, the normal approximation rate and the random weighting approximation rate of error distribution of the kernel estimator of conditional density function f(y|x) are studied. The results may be used to construct the confidence interval of f(y|x) .
文摘Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.
文摘A systematic methodology is proposed to deal with the weighted density approximation version of clas-sical density functional theory by employing the knowledge of radial distribution function of bulk fluid. The presentmethodology results from the concept of universality of the free energy density functional combined with the test particlemethod. It is shown that the new method is very accurate for the predictions of density distribution ofa hard sphere fluidat different confining geometries. The physical foundation of the present methodology is also applied to the quantumdensity functional theory.
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金supported by the National Natural Science Foundation of China(Grant No.52109156)the Science and Technology Project of the Jiangxi Provincial Education Department(Grant No.GJJ190970).
文摘Traditional methods for early warning of dam displacements usually assume that residual displacements follow a normal distribution.This assumption deviates from the reality,thereby affecting the reliability of early warning results and leading to misjudgments of dam displacement behavior.To solve this problem,this study proposed an early warning method using a non-normal distribution function.A new early warning index was developed using cumulative distribution function(CDF)values.The method of kernel density estimation was used to calculate the CDF values of residual displacements at a single point.The copula function was used to compute the CDF values of residual displacements at multiple points.Numerical results showed that,with residual displacements in a non-normal distribution,the early warning method proposed in this study accurately reflected the dam displacement behavior and effectively reduced the frequency of false alarms.This method is expected to aid in the safe operation of dams.
文摘Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.
文摘在航迹随机有限集的分布式多目标跟踪方法中,同一目标在不同传感器下估计航迹可能出现起始时间或航迹长度不一致的问题,提出一种基于航迹状态空间结构(state space structure,SSS)的分布式跟踪方法以及该方法的高斯混合模型实现。在基于加权算术平均融合准则的分布式多目标跟踪框架下,结合航迹概率假设密度滤波器与航迹基数概率假设密度滤波器,利用航迹SSS信息,将航迹随机有限集的信息融合问题分治为多个独立的单一线性空间内子随机有限集信息融合问题。仿真实验基于广义最优子模式匹配度量方法比较了该方法与多种跟踪方法的跟踪性能,该方法估计结果与真实航迹误差最小,表明了该方法的有效性。
文摘制造业集聚是城市发展的重要动力,同时也可能对生态环境产生负效应。论文拟以无锡市区为例,利用核密度函数(Kernel Density Distribution)对污染密集型制造业集聚程度进行评价,按照河流自然综合特征划分的环境单元进行污染物分布格局评价,在此基础上构建污染企业分布密度—COD排放量的双变量空间自相关模型,探讨制造业与河道污染物分布格局的定量关系,揭示制造业集聚和水污染的空间关联性。模型分析表明:无锡市区的污染密集型制造业呈现向郊区和环境非敏感区集聚的趋势,污染强度以主要运河为轴线向两翼地区逐渐衰减,二者空间格局的关联性存在行业差异性,污染物分布与纺织、石油化工业以及冶金业集聚和扩散格局的空间关联性较为显著,而与食品制造业和造纸印刷业的空间关联性则不显著。论文进一步根据产业集聚与污染格局的空间关联模式,将研究区域划分为高集聚—高污染、低集聚—低污染、低集聚—高污染、高集聚—低污染四种类型区,并提出相应的产业准入导向。本研究从空间效应角度为产业集聚与生态环境之间关联机理探讨提供新的视角,也可以作为制造业布局调整的科学依据。
