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A KERNEL ESTIMATOR OF A DENSITY FUNCTION IN MULTIVARIATE CASE FROM RANDOMLY CENSORED DATA 认领 引用
1
作者 周勇 《Acta Mathematica Scientia》 SCIE 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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Density Estimation Using Gumbel Kernel Estimator 认领 引用
2
作者 Javaria Ahmad Khan Atif Akbar 《Open Journal of Statistics》 2021年第2期319-328,共10页
In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of... In this article, our proposed kernel estimator, named as Gumbel kernel, which broadened the class of non-negative, asymmetric kernel density estimators. Such kernel estimator can be used in nonparametric estimation of the probability density function (pdf). When the density functions have limited bounded support on [0, ∞) and they are liberated of boundary bias, always non-negative and obtain the optimal rate of convergence for the mean integrated squared error (MISE). The bias, variance and the optimal bandwidth of the proposed estimators are investigated on theoretical grounds as well as on simulation basis. Further, the applicability of the proposed estimator is compared to Weibull kernel estimator, where performance of newly proposed kernel is outstanding. 展开更多
关键词 Asymmetrical Kernels Boundary Problems Density Estimation Flood Data Gumbel Kernel Estimator
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Improved estimator of the continuous-time kernel estimator 认领 引用
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作者 程建强 沈浩 何幼桦 《Journal of Shanghai University(English Edition)》 2010年第6期442-451,共10页
There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-sq... There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [0, T ]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. In a simulation study the results show the modified estimator is better than the original estimator in some cases. 展开更多
关键词 kernel density estimation mean-square continuous mean-square error （MSE）
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Asymptotic Confidence Bands for Copulas Based on the Local Linear Kernel Estimator 认领 引用
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作者 Diam Ba Cheikh Tidiane Seck Gane Samb Lo 《Applied Mathematics》 2015年第12期2077-2095,共19页
In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness c... In this paper, we establish asymptotically optimal simultaneous confidence bands for the copula function based on the local linear kernel estimator proposed by Chen and Huang [1]. For this, we prove under smoothness conditions on the derivatives of the copula a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We also show that the bias term converges uniformly to zero with a precise rate. The performance of these bands is illustrated by a simulation study. An application based on pseudo-panel data is also provided for modeling the dependence structure of Senegalese households’ expense data in 2001 and 2006. 展开更多
关键词 Copula Function Kernel Estimation Local Linear Estimator Uniform in Bandwidth Consistency Simultaneous Confidence Bands
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MODERATE DEVIATIONS AND LARGEDE VIATIONS FOR A TEST OF SYMMETRY BASED ON KERNEL DENSITY ESTIMATOR 认领 引用 被引量：5
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作者 何晓霞 高付清 《Acta Mathematica Scientia》 SCIE 2008年第3期665-674,共10页
Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove mod... Let fn be a non-parametric kernel density estimator based on a kernel function K. and a sequence of independent and identically distributed random variables taking values in R. The goal of this article is to prove moderate deviations and large deviations for the statistic sup ｜fn（x） - fn（-x） ｜. 展开更多
关键词 Symmetry test kernel estimator moderate deviations large deviations
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A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA 认领 引用 被引量：2
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作者 周勇 吴国富 李道纪 《Acta Mathematica Scientia》 SCIE 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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Some uniform convergence results for kernel estimators 认领 引用
7
作者 MENG MeiXia AI ChunRong 《Science China Mathematics》 SCIE EI 2013年第9期1945-1956,共12页
This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing... This paper derives some uniform convergence rates for kernel regression of some index functions that may depend on infinite dimensional parameter. The rates of convergence are computed for independent, strongly mixing and weakly dependent data respectively. These results extend the existing literature and are useful for the derivation of large sample properties of the estimators in some semiparametric and nonparametric models. 展开更多
关键词 uniform convergence kernel estimation convergence rate
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Large Deviations for a Test of Symmetry Based on Kernel Density Estimator of Directional Data 认领 引用
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作者 Mingzhou XU Kun CHENG 《Journal of Mathematical Research with Applications》 CSCD 2021年第6期639-647,共9页
Assume that fnis the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional... Assume that fnis the nonparametric kernel density estimator of directional data based on a kernel function K and a sequence of independent and identically distributed random variables taking values in d-dimensional unit sphere Sd-1.We established that the large deviation principle for{supx∈Sd-1|fn(x)-fn(-x)|,n≥1}holds if the kernel function is a function with bounded variation,and the density function f of the random variables is continuous and symmetric. 展开更多
关键词 symmetry test kernel density estimator directional data large deviations
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Central limit theorem for integrated square error of kernel estimators of spherical density 认领 引用 被引量：4
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作者 赵林城 吴成庆 《Science China Mathematics》 2001年第4期474-483,共10页
LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sumolimits_{i = 1}^n {K[(1 - x'X_i )/h... LetX 1,…,X n be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ? 1. Let $f_n (x) = n^{ - 1} c(h)\sumolimits_{i = 1}^n {K[(1 - x'X_i )/h^2 ]} $ be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off n under some mild conditions. 展开更多
关键词 central limit theorem directional data kernel estimate integrated square error
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Dynamic parameters prediction of the spatial deployable mechanism:a hybrid approach combining physics-based and data-driven models 认领 引用
10
作者 Yanhe Tao Qintao Guo +4 位作者 Jin Zhou Cheng Yi You Zhang Xiaofei Liu Ruiqi Chen 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2026年第5期535-549,共15页
Accurate prediction of the spatial mechanism's dynamic parameters in microgravity deployment simulations is crucial for identifying potential faults and ensuring precise gravitational compensation.Traditional engi... Accurate prediction of the spatial mechanism's dynamic parameters in microgravity deployment simulations is crucial for identifying potential faults and ensuring precise gravitational compensation.Traditional engineering models are often inaccurate,primarily because of insufficient experimental data and incomplete understanding of physical phenomena,which impedes model bias reduction in information-poor scenarios.We present a novel hybrid approach aimed at improving the predictive accuracy of the dynamic behavior of spatial deployable mechanisms.The graph convolutional network-temporal convolutional network(GCN-TCN)model,a type of deep learning architecture,is utilized for its expertise in forecasting spatio-temporal data through multi-step predictions.Next,the adaptive bandwidth kernel density estimation technique is applied to estimate the probability density function of residuals from the testing set of the GCN-TCN,quantifying predictive uncertainty.The predictive information is further refined using Bayesian inference,integrating a priori knowledge from physics-based models with data from data-driven models to yield robust posterior predictions.The proposed methodology is validated and shown to be robust through rigorous numerical simulations and experimental validation,demonstrating its ability to provide accurate and reliable predictions for the deployment of spatial mechanisms. 展开更多
关键词 Deep learning Kernel density estimation Data fusion Spatial deployable mechanisms Uncertainty quantification Hybrid approach Bayesian
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Spatial-temporal correlation between surface distress and internal damage in pavement structure 认领 引用
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作者 Yuhui Zhang Peiguo Yuan +5 位作者 Zhongping Wang Zepeng Fan Haotian Lyu Fujiao Tang Binglei Xie Dawei Wang 《Journal of Road Engineering》 EI CAS 2026年第2期232-244,共13页
A recurrent phenomenon is the reappearance of distress conditions on the same road section,both before and after maintenance interventions.The maintenance work essentially addresses the superficial symptoms rather tha... A recurrent phenomenon is the reappearance of distress conditions on the same road section,both before and after maintenance interventions.The maintenance work essentially addresses the superficial symptoms rather than the root causes,since the internal relationships between various forms of distress remain unclear.This study quantitatively evaluates the correlation between surface distress and internal defects based on field detection data and statistical methods,effectively complementing existing qualitative analytical method.Approximately 200 defect locations data were collected from the RIOHTrack full-scale ring road,and targeted evaluation metrics reflecting pavement performance were proposed.Then,the Ripley's K-function was employed to analyze the spatial aggregation of surface and internal cracks,and to further verify their macroscopic correlation during the spatio-temporal evolution process.Next,kernel density estimation and relative risk assessment were used to investigate the relationships between the surface distress and internal defects.Experimental results reveal that the loading position significantly affects surface distress,but exhibits no obvious correlation with hidden damage,and there is also no spatial aggregation phenomenon between them.However,for semi-rigid base asphalt pavement,internal cracks and surface cracks show a strong correlation,while demonstrating only a weak association with loading position.Finally,a sensitivity analysis was performed based on the results obtained at different distance thresholds,and r=0.5 m was designated as the optimal spatial correlation distance threshold.This threshold was then used to determine the pavement structure offering the best crack resistance performance,providing a key reference for the design and maintenance of heavy-duty highway pavements.This study provides a reference for road active maintenance and supports the transformation of maintenance strategies from passive response to active intervention. 展开更多
关键词 Pavement structure RIOHTrack Ripley's K-function Kernel density estimation Surface distress Internal defects
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APPROXIMATION RATES OF ERROR DISTRIBUTION OF DOUBLE KERNEL ESTIMATES OF CONDITIONAL DENSITY 认领 引用
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作者 XueLiugen CaiGuoliang 《Applied Mathematics(A Journal of Chinese Universities)》 2000年第4期425-432,共8页
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 con... 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
关键词 Conditional density function double kernel estimator random weighting method approximation rate.
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An Integrated Attention-BiLSTM Approach for Probabilistic Remaining Useful Life Prediction 认领 引用 被引量：1
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作者 Bo Zhu Enzhi Dong +3 位作者 Zhonghua Cheng Kexin Jiang Chiming Guo Shuai Yue 《Computers, Materials & Continua》 SCIE EI 2026年第4期966-984,共19页
Accurate prediction of remaining useful life serves as a reliable basis for maintenance strategies,effectively reducing both the frequency of failures and associated costs.As a core component of PHM,RUL prediction pla... Accurate prediction of remaining useful life serves as a reliable basis for maintenance strategies,effectively reducing both the frequency of failures and associated costs.As a core component of PHM,RUL prediction plays a crucial role in preventing equipment failures and optimizing maintenance decision-making.However,deep learning models often falter when processing raw,noisy temporal signals,fail to quantify prediction uncertainty,and face challenges in effectively capturing the nonlinear dynamics of equipment degradation.To address these issues,this study proposes a novel deep learning framework.First,a newbidirectional long short-termmemory network integrated with an attention mechanism is designed to enhance temporal feature extraction with improved noise robustness.Second,a probabilistic prediction framework based on kernel density estimation is constructed,incorporating residual connections and stochastic regularization to achieve precise RUL estimation.Finally,extensive experiments on the C-MAPSS dataset demonstrate that our method achieves competitive performance in terms of RMSE and Score metrics compared to state-of-the-artmodels.More importantly,the probabilistic output provides a quantifiablemeasure of prediction confidence,which is crucial for risk-informed maintenance planning,enabling managers to optimize maintenance strategies based on a quantifiable understanding of failure risk. 展开更多
关键词 Bidirectional long short-term memory network attention mechanism kernel density estimation remaining useful life prediction
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Stratospheric airship flight trajectory envelope prediction based on wind field uncertainty model 认领 引用
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作者 Lele QI Xixiang YANG +2 位作者 Xiaolong DENG Fangchao BAI Zhenyu MA 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2026年第6期389-405,共17页
Stratospheric airships,as typical low-speed near space aircraft,exhibit great potential in the fields of communication relay and high-altitude monitoring.However,due to the considerable uncertainty of the external win... Stratospheric airships,as typical low-speed near space aircraft,exhibit great potential in the fields of communication relay and high-altitude monitoring.However,due to the considerable uncertainty of the external wind field environment,the deviation of stratospheric airship flight trajectory increases.To effectively predict the envelope of stratospheric airship flight trajectory,this paper proposes an innovative trajectory envelope prediction method to offer a new perspective on related research.By establishing wind field uncertainty model including both wind speed uncertainty and wind direction uncertainty,stratospheric airship trajectories are obtained under four extreme wind fields,and the trajectory envelope is generated using the Alpha-Shape method.Furthermore,the adaptive bandwidth kernel density estimation method is introduced to quantify the trajectory distribution probability,providing an intuitive description of the trajectory distribution probability.The simulation results show that the proposed methods can effectively predict the stratospheric airship flight trajectory envelope and describe trajectory distribution characteristics,supporting mission planning,risk assessment,and energy-management strategy selection for stratospheric airship flight tests. 展开更多
关键词 Alpha-Shape Flight trajectory envelope Kernel density estimation Stratospheric airship Trajectory distribution probability Worst-to-worst
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A physics-guided explainable machine learning framework for residual-based performance deviation detection and probabilistic severity assessment in photovoltaic systems 认领 引用
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作者 Roby Mohajon Shuva Chandra Sarker +5 位作者 Md Amzad Sadik Abid Simanta Datta Ronobir Abid Kamal Rumi Shimul Chakraborty Adiba Juoairia Nur Mohammad 《Clean Energy》 EI CSCD 2026年第3期143-163,共21页
Monitoring photovoltaic plants entails the use of techniques that are physically meaningful for detecting deviations in the observed behavior from what is expected.Data-driven methods frequently suffer from poor physi... Monitoring photovoltaic plants entails the use of techniques that are physically meaningful for detecting deviations in the observed behavior from what is expected.Data-driven methods frequently suffer from poor physical consistency,whereas physics-based models may fail to account for practical variations in operational behavior.In this study,we present a physics-driven machine learning methodology for estimating fault severity in grid-connected photovoltaic systems.The proposed methodology combines a calibrated PVsyst-based expected power generation model and supervisory control and data acquisition data collected from two 56.32 kilowatt-peak photovoltaic plants.Linear bias correction of the simulation results enhanced the correlation between the predicted and actual power generation levels,with coefficient of determination values of 0.685 and 0.566 for Plants 1 and 2,respectively.The Gaussian mixture model approach coupled with Bayesian information criterion tuning revealed the statistical fault-severity threshold,Rnorm=−0.161,for the discrimination between normal and severe states.For the prediction task,a random forest classifier was trained on seven physics-aware variables and achieved accuracy and macro-F1 scores of 0.920 and 0.907,respectively,through walk-forward validation.Comparative benchmarking with other classifiers,including XGBoost,support vector machine,and decision tree algorithms,showed a better classification performance balance.In addition,the explainability study verified the importance of irradiance,expected power,and conversion efficiency metrics. 展开更多
关键词 photovoltaic performance monitoring physics-Guided machine learning bias-Corrected residual analysis Gaussian mixture model walk-Forward cross-Validation SHAP explainability MDI feature importance kernel density estimation
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ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA 认领 引用 被引量：2
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作者 陈平 《Acta Mathematica Scientia》 SCIE 1999年第3期321-331,共11页
This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author als... This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet. 展开更多
关键词 partial linear model censored data local linear smoothing cross-validation kernel estimator
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Enhancing microseismic/acoustic emission source localization accuracy with an outlier-robust kernel density estimation approach 认领 引用 被引量：8
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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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Spatiotemporal Patterns of Road Network and Road Development Pri-ority in Three Parallel Rivers Region in Yunnan,China:An Evaluation Based on Modified Kernel Distance Estimate 认领 引用 被引量：7
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作者 YING Lingxiao SHEN Zehao +3 位作者 CHEN Jiding FANG Rui CHEN Xueping JIANG Rui 《Chinese Geographical Science》 SCIE CSCD 2014年第1期39-49,共11页
Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road servic... Road network is a critical component of public infrastructure,and the supporting system of social and economic development.Based on a modified kernel density estimate(KDE)algorithm,this study evaluated the road service capacity provided by a road network composed of multi-level roads(i.e.national,provincial,county and rural roads),by taking account of the differences of effect extent and intensity for roads of different levels.Summarized at town scale,the population burden and the annual rural economic income of unit road service capacity were used as the surrogates of social and economic demands for road service.This method was applied to the road network of the Three Parallel River Region,the northwestern Yunnan Province,China to evaluate the development of road network in this region.In results,the total road length of this region in 2005 was 3.70×104km,and the length ratio between national,provincial,county and rural roads was 1∶2∶8∶47.From 1989 to 2005,the regional road service capacity increased by 13.1%,of which the contributions from the national,provincial,county and rural roads were 11.1%,19.4%,22.6%,and 67.8%,respectively,revealing the effect of′All Village Accessible′policy of road development in the mountainous regions in the last decade.The spatial patterns of population burden and economic requirement of unit road service suggested that the areas farther away from the national and provincial roads have higher road development priority(RDP).Based on the modified KDE model and the framework of RDP evaluation,this study provided a useful approach for developing an optimal plan of road development at regional scale. 展开更多
关键词 road network kernel density estimate（KDE） road service road development priority（RDP） Three Parallel Rivers Region China
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Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation 认领 引用 被引量：5
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作者 Peizhe Xin Ying Liu +2 位作者 Nan Yang Xuankun Song Yu Huang 《Global Energy Interconnection》 EI 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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Statistical Characteristics Analysis Based on F/A-XX Fighter Using Adapative Kernel Density Estimation Algorithm 认领 引用 被引量：3
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作者 FU Li JIANG Guanwu HUANG Quanjun 《Journal of Shanghai Jiaotong university(Science)》 EI 2024年第6期1202-1210,共9页
The sixth-generation fighter has superior stealth performance,but for the traditional kernel density estimation(KDE),precision requirements are difficult to satisfy when dealing with the fluctuation characteristics of... The sixth-generation fighter has superior stealth performance,but for the traditional kernel density estimation(KDE),precision requirements are difficult to satisfy when dealing with the fluctuation characteristics of complex radar cross section(RCS).To solve this problem,this paper studies the KDE algorithm for F/AXX stealth fighter.By considering the accuracy lack of existing fixed bandwidth algorithms,a novel adaptive kernel density estimation(AKDE)algorithm equipped with least square cross validation and integrated squared error criterion is proposed to optimize the bandwidth.Meanwhile,an adaptive RCS density estimation can be obtained according to the optimized bandwidth.Finally,simulations verify that the estimation accuracy of the adaptive bandwidth RCS density estimation algorithm is more than 50%higher than that of the traditional algorithm.Based on the proposed algorithm(i.e.,AKDE),statistical characteristics of the considered fighter are more accurately acquired,and then the significant advantages of the AKDE algorithm in solving cumulative distribution function estimation of RCS less than 1 m2 are analyzed. 展开更多
关键词 radar cross section(RCS) kernel density estimation(KDE) statistical properties
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