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
In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly...In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.展开更多
The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial charact...The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial characteristics is presented to estimate road traffic states. Firstly, the representative road traffic state data were extracted to establish the reference sequences of road traffic running characteristics(RSRTRC). Secondly, the spatial road traffic state data sequence was selected and the kernel function was constructed, with which the spatial road traffic data sequence could be mapped into a high dimensional feature space. Thirdly, the referenced and current spatial road traffic data sequences were extracted and the Euclidean distances in the feature space between them were obtained. Finally, the road traffic states were estimated from weighted averages of the selected k road traffic states, which corresponded to the nearest Euclidean distances. Several typical links in Beijing were adopted for case studies. The final results of the experiments show that the accuracy of this algorithm for estimating speed and volume is 95.27% and 91.32% respectively, which prove that this road traffic states estimation approach based on kernel-KNN matching of road traffic spatial characteristics is feasible and can achieve a high accuracy.展开更多
In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These res...In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These results give sharp pointwise rates of strong consistency ofthese estimators.展开更多
The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar result...The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.展开更多
基金Research supported by National Natural Science Foundation of China.
文摘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).
基金Supported by the National Natural Science Foundation of China(Grant Nos.11671012,11871072,11701004 and 11701005)the Natural Science Foundation of Anhui Province(Grant No.1508085J06)+2 种基金the Key Projects for Academic Talent of Anhui Province(Grant No.gxbjZD2016005)the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province(Grant No.2017H123)the Research Teaching Model Curriculum of Anhui University(Grant No.xjyjkc1407)
文摘In this paper, we mainly study the consistency of the nearest neighbor estimator of the density function based on asymptotically almost negatively associated samples. The weak consistency,strong consistency, uniformly strong consistency and the convergence rates are established under some mild conditions. As applications, we further investigate the strong consistency and the rate of strong consistency for hazard rate function estimator.
基金Projects(LQ16E080012,LY14F030012)supported by the Zhejiang Provincial Natural Science Foundation,ChinaProject(61573317)supported by the National Natural Science Foundation of ChinaProject(2015001)supported by the Open Fund for a Key-Key Discipline of Zhejiang University of Technology,China
文摘The accurate estimation of road traffic states can provide decision making for travelers and traffic managers. In this work,an algorithm based on kernel-k nearest neighbor(KNN) matching of road traffic spatial characteristics is presented to estimate road traffic states. Firstly, the representative road traffic state data were extracted to establish the reference sequences of road traffic running characteristics(RSRTRC). Secondly, the spatial road traffic state data sequence was selected and the kernel function was constructed, with which the spatial road traffic data sequence could be mapped into a high dimensional feature space. Thirdly, the referenced and current spatial road traffic data sequences were extracted and the Euclidean distances in the feature space between them were obtained. Finally, the road traffic states were estimated from weighted averages of the selected k road traffic states, which corresponded to the nearest Euclidean distances. Several typical links in Beijing were adopted for case studies. The final results of the experiments show that the accuracy of this algorithm for estimating speed and volume is 95.27% and 91.32% respectively, which prove that this road traffic states estimation approach based on kernel-KNN matching of road traffic spatial characteristics is feasible and can achieve a high accuracy.
文摘In this paper we study the estimation of the regression function.We establish a law ofthe iterated logarithm for the random window-width kernel estimator and,as an application,fora nearest neighbor estimator.These results give sharp pointwise rates of strong consistency ofthese estimators.
文摘The nearest neighbor (n.n.) and its related methods are widely used in density and hazard function estimations. Even though the asymptotic normality of the n.n. density estimate is well known (see [1]), similar results for the n.n. hazard estimate have not been shown in the literature. In this paper, we develop a different approach to deal with the n.n. type estimator. For a mixed censorship-truneation model, we show that, under mild conditions, the n. n. estimate can be approximated by an estimate formed with a proper fixed bandwidth sequence and derive the asymptotic normality as a consequence.
