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A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA
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作者 周勇 《Acta Mathematica Scientia》 SCIE CSCD 1996年第2期170-180,共11页
A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error ... A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error of the estimator are studied. 展开更多
关键词 kernel density estimator asymptotic normality product-limit estimator mean square error and censored data.
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A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA 被引量:1
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作者 周勇 吴国富 李道纪 《Acta Mathematica Scientia》 SCIE CSCD 2006年第4期585-594,共10页
A kernel-type estimator of the quantile function Q(p) = inf{t:F(t) ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o... A kernel-type estimator of the quantile function Q(p) = inf{t:F(t) ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent. 展开更多
关键词 Truncated data Product-limits quantile function kernel estimator Bahadur representation
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ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE
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作者 林正炎 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期345-350,共6页
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
关键词 associated random variables negatively associated random variables kernel estimate of a density function central limit theorem
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Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach 被引量:1
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作者 Jie Chen Huiqiong Huang +4 位作者 Yichao Rui Yuanyuan Pu Sheng Zhang Zheng Li Wenzhong Wang 《International Journal of Mining Science and Technology》 SCIE EI CAS CSCD 2024年第7期943-956,共14页
Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust l... Monitoring sensors in complex engineering environments often record abnormal data,leading to significant positioning errors.To reduce the influence of abnormal arrival times,we introduce an innovative,outlier-robust localization method that integrates kernel density estimation(KDE)with damping linear correction to enhance the precision of microseismic/acoustic emission(MS/AE)source positioning.Our approach systematically addresses abnormal arrival times through a three-step process:initial location by 4-arrival combinations,elimination of outliers based on three-dimensional KDE,and refinement using a linear correction with an adaptive damping factor.We validate our method through lead-breaking experiments,demonstrating over a 23%improvement in positioning accuracy with a maximum error of 9.12 mm(relative error of 15.80%)—outperforming 4 existing methods.Simulations under various system errors,outlier scales,and ratios substantiate our method’s superior performance.Field blasting experiments also confirm the practical applicability,with an average positioning error of 11.71 m(relative error of 7.59%),compared to 23.56,66.09,16.95,and 28.52 m for other methods.This research is significant as it enhances the robustness of MS/AE source localization when confronted with data anomalies.It also provides a practical solution for real-world engineering and safety monitoring applications. 展开更多
关键词 Microseismic source/acoustic emission(MS/aE) kernel density estimation(KDE) Damping linear correction Source location abnormal arrivals
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Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation 被引量:4
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作者 Peizhe Xin Ying Liu +2 位作者 Nan Yang Xuankun Song Yu Huang 《Global Energy Interconnection》 2020年第3期247-258,共12页
In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met... In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE. 展开更多
关键词 Moving average method Signal decomposition Wind power fluctuation characteristics kernel density estimation Constrained order optimization
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DENSITY ESTIMATES FOR SOLUTIONS OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
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作者 Nguyen Tien DUNG Ta Cong SON +2 位作者 Tran Manh CUONG Nguyen Van TAN Trinh Nhu QUYNH 《Acta Mathematica Scientia》 SCIE CSCD 2019年第4期955-970,共16页
In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the d... In this article, we investigate the density of the solution to a class of stochastic functional differential equations by means of Malliavin calculus. Our aim is to provide upper and lower Gaussian estimates for the density. 展开更多
关键词 STOCHaSTIC functionaL DIFFERENTIaL EQUaTIONS density ESTIMaTES Malliavin CaLCULUS
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On the L_p Convergence Rate of Kernel Estimates for the Nonparametric Regression Function
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作者 薛留根 《Chinese Quarterly Journal of Mathematics》 CSCD 1992年第1期37-43,共7页
Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a p... Let (X,Y) be an R^d×R^1 valued random vector (X_1,Y_1),…, (X_n,Y_n) be a random sample drawn from (X,Y), and let E|Y|<∞. The regression function m(x)=E(Y|X=x) for x∈R^d is estimated by where, and h_n is a positive number depending upon n only, nad K is a given nonnegative function on R^d. In the paper, we study the L_p convergence rate of kernel estimate m_n(x) of m(x) in suitable condition, and improve and extend the results of Wei Lansheng. 展开更多
关键词 regression function L convergence rate kernel estimate
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Strong Consistency for the Kernal Estimates of the Random Window Width of the Density Function and its Derivatives Under Φ-Mixing Samples
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作者 樊家琨 《Chinese Quarterly Journal of Mathematics》 CSCD 1993年第3期52-56,共5页
In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-m... In the paper,we study the strong uniform consistency for the kernal estimates of random window w■th of density function and its derivatives under the condition that the sequence{X_n}of the ■ are the identically Φ-mixing random variabks. 展开更多
关键词 Φ-mixing sample probability density function random window width kemal estimate strng uniform consistency
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A LAW OF THE ITERATED LOGARITHM FOR NEAREST NEIGHBOR ESTIMATION OF MULTIVARIATE DENSITY FUNCTION
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作者 洪圣岩 陈规景 +1 位作者 孔繁超 高集体 《Acta Mathematica Scientia》 SCIE CSCD 1992年第4期472-478,共7页
Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we est... Let X be a d-dimensional random vector with unknown density function f(z) = f (z1, ..., z(d)), and let f(n) be teh nearest neighbor estimator of f proposed by Loftsgaarden and Quesenberry (1965). In this paper, we established the law of the iterated logarithm of f(n) for general case of d greater-than-or-equal-to 1, which gives the exact pointwise strong convergence rate of f(n). 展开更多
关键词 a LaW of THE ITERaTED LOGaRITHM FOR NEaREST NEIGHBOR ESTIMaTION of MULTIVaRIaTE density function exp
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Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences 被引量:1
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作者 薛留根 李雪臣 马全甫 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第2期1-10, ,共10页
In the paper,we study the strong convergence rates of double kernel estimates of conditional density under stationary sequences.
关键词 conditional density double kernel estimates strong convergence rates stationary sequences
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基于Copula函数的框支剪力墙基础隔震结构地震易损性分析
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作者 孙倩龙 何沛祥 《合肥工业大学学报(自然科学版)》 北大核心 2025年第2期267-273,共7页
针对经典构件地震易损性分析方法的不足,文章将Copula函数引入到构件地震易损性分析中,提出一种基于Copula函数的构件地震易损性分析方法。在地震易损性分析框架的基础上,通过引入非参数核密度估计和Copula函数建立地震动强度和构件地... 针对经典构件地震易损性分析方法的不足,文章将Copula函数引入到构件地震易损性分析中,提出一种基于Copula函数的构件地震易损性分析方法。在地震易损性分析框架的基础上,通过引入非参数核密度估计和Copula函数建立地震动强度和构件地震需求的联合概率分布函数,使地震易损性分析无需人为假定易损性函数分布形式。以某框支剪力墙基础隔震结构为工程背景,基于Copula函数的地震易损性分析方法建立结构各构件的易损性曲线,并与常用构件易损性分析方法的计算结果进行比较,验证了该方法的可行性。研究结果表明,该方法有助于优化框支剪力墙隔震结构易损性曲线的建模过程,为地震易损性研究提供新的思路和方法。 展开更多
关键词 框支剪力墙 基础隔震 地震易损性 COPULa函数 核密度估计
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我国护理人力资源区域差异的演变特征——基于Dagum基尼系数分解和Kernel核密度估计的实证研究
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作者 王佳怡 沈芸 +2 位作者 朱燕 宋天敕 陈洁婷 《军事护理》 CSCD 北大核心 2024年第11期90-94,共5页
目的分析我国护理人力资源的区域差异及分布动态演进,为我国护理人力资源的合理配置和规划提供参考。方法基于2011-2022年省级护理人力资源面板数据,通过测算Kernel密度和Dagum基尼系数对我国护理人力资源的区域差异及分布动态演进进行... 目的分析我国护理人力资源的区域差异及分布动态演进,为我国护理人力资源的合理配置和规划提供参考。方法基于2011-2022年省级护理人力资源面板数据,通过测算Kernel密度和Dagum基尼系数对我国护理人力资源的区域差异及分布动态演进进行分析评价。结果2011-2022年,在空间分布上,全国及各地区护理人力资源总量呈增加趋势,各区域差异逐步降低,且两极化特征明显;在区域差异上,我国护理人力资源总体差异均值为0.1149;区域内呈东部>西部>中部>东北区域的梯度逐步递增趋势;区域间差异占总体差异的40.61%。结论全国护理人力资源总体差异处于相对合理状态,区域间差异是主要来源,均等化水平逐步提升;政府应针对各区域精准施策,进一步稳定护理人力资源队伍,完善护理人力资源结构以促进护理人力资源的优质均衡发展。 展开更多
关键词 护理人力资源 区域差异 Dagum基尼系数 kernel密度估计
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Improved Algorithm of Variable Bandwidth Kernel Particle Filter
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作者 葛欣 丁恩杰 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第3期303-307,共5页
Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is fa... Aiming at the large cost of calculating variable bandwidth kernel particle filter and the high complexity of its algorithm,a self-adjusting kernel function particle filter is presented. Kernel density estimation is facilitated to iterate and obtain new particle set. And the standard deviation of particle is introduced in the kernel bandwidth. According to the characteristics of particle distribution,the bandwidth is dynamically adjusted,and the particle distribution can thus be more close to the posterior probability density model of the system. Meanwhile,the kernel density is used to estimate the weight of updating particle and the system state. The simulation results show the feasibility and effectiveness of the proposed algorithm. 展开更多
关键词 particle filter kernel density estimation kernel bandwidth SELF-aDJUSTING
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ESSENTIAL RELATIONSHIP BETWEEN DOMAIN-BASED ONE-CLASS CLASSIFIERS AND DENSITY ESTIMATION 被引量:2
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作者 陈斌 李斌 +1 位作者 冯爱民 潘志松 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2008年第4期275-281,共7页
One-class support vector machine (OCSVM) and support vector data description (SVDD) are two main domain-based one-class (kernel) classifiers. To reveal their relationship with density estimation in the case of t... One-class support vector machine (OCSVM) and support vector data description (SVDD) are two main domain-based one-class (kernel) classifiers. To reveal their relationship with density estimation in the case of the Gaussian kernel, OCSVM and SVDD are firstly unified into the framework of kernel density estimation, and the essential relationship between them is explicitly revealed. Then the result proves that the density estimation induced by OCSVM or SVDD is in agreement with the true density. Meanwhile, it can also reduce the integrated squared error (ISE). Finally, experiments on several simulated datasets verify the revealed relationships. 展开更多
关键词 one-class support vector machine(OCSVM) support vector data description(SVDD) kernel density estimation
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Data-driven source-load robust optimal scheduling of integrated energy production unit including hydrogen energy coupling 被引量:2
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作者 Jinling Lu Dingyue Huang Hui Ren 《Global Energy Interconnection》 EI CSCD 2023年第4期375-388,共14页
A robust low-carbon economic optimal scheduling method that considers source-load uncertainty and hydrogen energy utilization is developed.The proposed method overcomes the challenge of source-load random fluctuations... A robust low-carbon economic optimal scheduling method that considers source-load uncertainty and hydrogen energy utilization is developed.The proposed method overcomes the challenge of source-load random fluctuations in integrated energy systems(IESs)in the operation scheduling problem of integrated energy production units(IEPUs).First,to solve the problem of inaccurate prediction of renewable energy output,an improved robust kernel density estimation method is proposed to construct a data-driven uncertainty output set of renewable energy sources statistically and build a typical scenario of load uncertainty using stochastic scenario reduction.Subsequently,to resolve the problem of insufficient utilization of hydrogen energy in existing IEPUs,a robust low-carbon economic optimal scheduling model of the source-load interaction of an IES with a hydrogen energy system is established.The system considers the further utilization of energy using hydrogen energy coupling equipment(such as hydrogen storage devices and fuel cells)and the comprehensive demand response of load-side schedulable resources.The simulation results show that the proposed robust stochastic optimization model driven by data can effectively reduce carbon dioxide emissions,improve the source-load interaction of the IES,realize the efficient use of hydrogen energy,and improve system robustness. 展开更多
关键词 Hydrogen energy coupling DaTa-DRIVEN Robust kernel density estimation Robust optimization Integrated demand response
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Analysis on Potential Conflict Frequency of Intersected Air Routes in Terminal Airspace Design 被引量:1
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作者 王超 韩邦村 刘菲 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第5期580-588,共9页
In order to obtain accurate conflict risks in terminal airspace design,the concept and calculation model of potential conflict frequency for intersected routes are proposed.Conflict frequency is represented by the pro... In order to obtain accurate conflict risks in terminal airspace design,the concept and calculation model of potential conflict frequency for intersected routes are proposed.Conflict frequency is represented by the product of horizontal conflict frequency and vertical conflict probability.The horizontal conflict frequency is derived from the probability density distribution of conflicts in a period of time.Based on the recorded radar trajectory data,the concept and model of ROUTE distance are proposed,and the probability density function of aircraft height at a specified ROUTE distance is deduced by kernel density estimation.Furthermore,vertical conflict probability and its horizontal distribution are achieved.Examples of three intersected arrival and departure route design schemes are studied.Compared with scheme 1,the conflict frequency values of the other two improved schemes decrease to53% and 24%,respectively.The results show that the model can quantify potential conflict frequency of intersected routes. 展开更多
关键词 air traffic management terminal airspace design horizontal conflict frequency vertical conflict proba-bility kernel density estimation(KDE)
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基于KANN-DBSCAN带宽优化的核密度估计载荷谱外推
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作者 张金保 杨永乐 +4 位作者 张志飞 彭良峰 林伟雄 张佑源 徐中明 《汽车工程》 EI CSCD 北大核心 2024年第11期2100-2109,共10页
针对核密度估计载荷外推全局固定带宽的局限性,提出一种基于KANN-DBSCAN(K-average nearest neighbor density-based spatial clustering of applications with noise)改进带宽取值的核密度估计(kernel density estimation, KDE)载荷外... 针对核密度估计载荷外推全局固定带宽的局限性,提出一种基于KANN-DBSCAN(K-average nearest neighbor density-based spatial clustering of applications with noise)改进带宽取值的核密度估计(kernel density estimation, KDE)载荷外推方法。通过KANN-DBSCAN聚类算法对载荷数据进行分组聚类,采用拇指法求得不同簇间的最优带宽,然后进行核密度估计,再采用蒙特卡洛模拟进行外推。以某电动汽车在用户道路的实测载荷数据为应用对象,对外推方法的合理性进行检验。从统计参数检验量、拟合度检验和伪损伤检验3个指标对外推效果进行评估。结果表明:相比固定带宽的核密度估计外推方法,基于KANN-DBSCSN核密度估计的外推方法获得的外推载荷在统计参数上与实测载荷更为接近,均值、标准差和最大值的误差分别仅为1.9%、 4.3%和1.9%;幅值累计频次曲线拟合度R2均大于0.99,伪损伤均接近1。结果验证了该聚类方法在核密度估计载荷外推的有效性,有助于编制汽车在用户道路上的载荷谱,为具有相似载荷分布特点的机械零部件载荷外推提供了参考。 展开更多
关键词 载荷外推 聚类 核密度估计 拇指法 蒙特卡洛模拟
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基于Stacking集成的RF-ET-KDE烧结过程物理指标区间预测模型
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作者 康增鑫 陈进朝 +1 位作者 王金杨 吴朝霞 《东北大学学报(自然科学版)》 EI CAS CSCD 北大核心 2024年第10期1369-1378,共10页
由于烧结过程中存在众多不确定性因素,使得机理分析和点预测结果的可靠性不足.基于此提出随机森林-极限树-核密度估计(random forest-extreme tree-kernel density estimation,RF-ET-KDE)算法对物理指标(粒度、水分)进行区间预测.首先,... 由于烧结过程中存在众多不确定性因素,使得机理分析和点预测结果的可靠性不足.基于此提出随机森林-极限树-核密度估计(random forest-extreme tree-kernel density estimation,RF-ET-KDE)算法对物理指标(粒度、水分)进行区间预测.首先,采用数据预处理和特征选择操作筛选出最适合建模的特征变量.其次,使用基于Stacking的RF-ET算法对指标进行点预测,该算法使得模型有较高的准确性和泛化性.然后,采用KDE算法计算指标的预测误差,得到了一定置信水平下的分布区间和区间预测结果.最后,用所建模型与其余组合模型进行对比.结果表明,RF-ET算法有较高的点预测效果,KDE算法可以很好地量化指标的误差,可以得到较高可靠度的区间预测结果. 展开更多
关键词 烧结过程 随机森林-极限树 核密度估计 物理指标 区间预测
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基于LASSO回归和QRLSTM的来水预测方法研究
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作者 何常新 彭旭 +3 位作者 方福东 杜灿阳 曾庚运 胡千帝 《人民长江》 北大核心 2024年第11期138-145,165,共9页
精准的河流断面来水流量预测对于水资源配置管理、洪水预警和防灾减灾、生态保护和水力发电工程规划有着重要意义。为了提高单一来水流量预测模型的预测精度,采用LASSO回归算法结合分位数回归长短期记忆神经网络(QRLSTM)以及核密度估计(... 精准的河流断面来水流量预测对于水资源配置管理、洪水预警和防灾减灾、生态保护和水力发电工程规划有着重要意义。为了提高单一来水流量预测模型的预测精度,采用LASSO回归算法结合分位数回归长短期记忆神经网络(QRLSTM)以及核密度估计(KDE)算法,提出了一种来水流量预测方法(LASSO-QRLSTM)。首先采用LASSO回归从高维来水特征向量中提取关键的解释变量,以降低解释变量与被解释变量之间非线性关系的复杂程度;接着建立QRLSTM来水流量预测模型,以获得不同分位点下的分位数预测值;进而利用KDE拟合概率密度函数,获得未来的来水流量可能值以及相应的概率,得出最终预测结果。将提出的模型应用于广东省西江关键断面和高要水文站的来水流量预测,并与LASSO-QRNN、LASSO-GBDT、QRLSTM、QRNN、GBDT模型进行对比。结果表明:(1)结合LASSO回归的混合预测模型预测效果均好于单一的QRLSTM、QRNN、GBDT模型。(2)提出的LASSO-QRLSTM模型在对思贤滘断面流量预测中的RMSE为1 804.270 m^(3)/s,NSE值达0.973;在概率性指标方面,LASSO-QRLSTM模型的连续分级概率评分(CRPS)和弹球损失(PL)值分别为842.618和465.964,各项评价指标均为最佳,在对比模型中表现出最好的预测效果,特别是在极值处具有更好的拟合效果和更窄的概率预测区间,表现出该模型在河流来水流量预测中的独特优势。(3)在后续对高要水文站来水流量的预测中,其预测性能得到进一步验证,展现出良好的适应性和稳定性。研究成果可为精准的水文预测和水资源优化配置提供参考。 展开更多
关键词 来水流量预测 LaSSO回归 分位数回归 长短期记忆神经网络 核密度估计 西江
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乡村振兴发展水平测度、时空格局与区域差异
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作者 张红岩 彭勃 《现代农业研究》 2025年第2期50-61,共12页
文章基于乡村振兴的内涵从产业兴旺、生态宜居、乡风文明、治理有效、生活富裕五个维度,使用2011—2022年我国31个省、自治区、直辖市的面板数据构建乡村振兴发展水平综合评价体系,通过熵权法对乡村振兴发展水平进行统计测度,使用Kerne... 文章基于乡村振兴的内涵从产业兴旺、生态宜居、乡风文明、治理有效、生活富裕五个维度,使用2011—2022年我国31个省、自治区、直辖市的面板数据构建乡村振兴发展水平综合评价体系,通过熵权法对乡村振兴发展水平进行统计测度,使用Kernel密度估计法、莫兰指数I和Dagum基尼系数分解方法对其时空格局与区域差异进行分析。研究发现:(1)我国乡村振兴发展水平整体呈现上升趋势,其中中部地区发展水平最高西部地区最低。(2)我国乡村振兴发展水平存在明显的区域发展不平衡现象,但该现象正在逐步消失。其中导致区域发展不平衡的主要原因为区域间差异。(3)全国和三大区域的核密度曲线主峰位置均呈现右移趋势,并东、中、西部地区均存在极分化现象。(4)乡村振兴发展水平存在显著的空间相关性,呈现“高-高“”低-低”集聚的现象。 展开更多
关键词 乡村振兴 时空格局 区域差异 莫兰指数I kernel密度估计 Dagum基尼系数
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