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
Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed ...Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].展开更多
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
In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bia...In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.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
In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. wh...In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.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
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
The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many...The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many inves<span style="font-family:Verdana;">tigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a </span><span style="font-family:Verdana;">heavy-tailed distribution is discussed when some functional random covariate (</span><i><span style="font-family:Verdana;">i.e.</span></i><span style="font-family:Verdana;"> valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.</span>展开更多
There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally b...There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally best among possible background models. For KDE, the selection of kernel functions and their bandwidths greatly influence the performance. There were few attempts to compare the adequacy of functions for KDE. In this paper, we evaluate the performance of various functions for KDE. Functions tested include almost everyone cited in the literature and a new function, Laplacian of Gaussian(LoG) is also introduced for comparison. All tests were done on real videos with vary-ing background dynamics and results were analyzed both qualitatively and quantitatively. Effect of different bandwidths was also investigated.展开更多
锂电池健康状态(state of health, SOH)的退化过程在一定程度上是一个非平稳随机过程,使得当前多数点估计机器学习方法在实际应用中受到限制。基于贝叶斯理论的高斯过程回归(Gaussian process regression,GPR),因可输出估计结果的不确定...锂电池健康状态(state of health, SOH)的退化过程在一定程度上是一个非平稳随机过程,使得当前多数点估计机器学习方法在实际应用中受到限制。基于贝叶斯理论的高斯过程回归(Gaussian process regression,GPR),因可输出估计结果的不确定性,近年来在锂电池SOH区间估计中得到广泛应用。然而,GPR的性能很大程度上取决于其核函数的选择,当前研究多凭借经验选用固定单一核函数,无法适应不同的数据集。为此,本文提出一种基于自适应最优组合核函数GPR的锂电池SOH区间估计方法。该方法首先从电池充放电数据中提取出多个健康因子(health factor, HF),并采用皮尔森相关系数法优选出6个与SOH高度相关的健康因子作为模型的输入。然后,在当前常用的7个核函数集合上,通过两两随机组合构造新的组合核函数,并利用交叉验证自适应优选出最优组合核函数。采用3个不同数据集对所提方法进行了验证,结果表明:本文方法具有出色的SOH区间估计性能。在3个公开数据集上,平均区间宽度指标在0.0509以内,平均区间分数大于-0.0004,均方根误差小于0.0181。展开更多
长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度...长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度分析、实地调查验证等方法,识别长春市中心城区城市功能类型。结果表明:单一功能区中,商业功能区数量最多,居住功能区最少;主导—混合功能区中的商业主导功能区及交通主导功能区形成对商业聚集区与轨道交通系统的重要补充;细分—混合功能区特征显示功能混合程度从市中心向周边逐渐加大。经验证,城市功能识别结果符合长春市实际,由此提出对策建议:未来长春市中心城区应注重多中心发展格局,并加强绿地空间和公共服务设施建设。展开更多
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
文摘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.
基金supported by National Natural Science Foundation of China(No.11301084)Natural Science Foundation of Fujian Province(No.2014J01010)
文摘Under some mild conditions, we derive the asymptotic normality of the Nadaraya-Watson and local linear estimators of the conditional hazard function for left-truncated and dependent data. The estimators were proposed by Liang and Ould-Sa?d [1]. The results confirm the guess in Liang and Ould-Sa?d [1].
基金Zhou's research was partially supported by the NNSF of China (10471140, 10571169)Wu's research was partially supported by NNSF of China (0571170)
文摘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.
文摘In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.
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In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.
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.
文摘The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many inves<span style="font-family:Verdana;">tigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a </span><span style="font-family:Verdana;">heavy-tailed distribution is discussed when some functional random covariate (</span><i><span style="font-family:Verdana;">i.e.</span></i><span style="font-family:Verdana;"> valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.</span>
文摘There have been vast amount of studies on background modeling to detect moving objects. Two recent reviews[1,2] showed that kernel density estimation(KDE) method and Gaussian mixture model(GMM) perform about equally best among possible background models. For KDE, the selection of kernel functions and their bandwidths greatly influence the performance. There were few attempts to compare the adequacy of functions for KDE. In this paper, we evaluate the performance of various functions for KDE. Functions tested include almost everyone cited in the literature and a new function, Laplacian of Gaussian(LoG) is also introduced for comparison. All tests were done on real videos with vary-ing background dynamics and results were analyzed both qualitatively and quantitatively. Effect of different bandwidths was also investigated.
文摘锂电池健康状态(state of health, SOH)的退化过程在一定程度上是一个非平稳随机过程,使得当前多数点估计机器学习方法在实际应用中受到限制。基于贝叶斯理论的高斯过程回归(Gaussian process regression,GPR),因可输出估计结果的不确定性,近年来在锂电池SOH区间估计中得到广泛应用。然而,GPR的性能很大程度上取决于其核函数的选择,当前研究多凭借经验选用固定单一核函数,无法适应不同的数据集。为此,本文提出一种基于自适应最优组合核函数GPR的锂电池SOH区间估计方法。该方法首先从电池充放电数据中提取出多个健康因子(health factor, HF),并采用皮尔森相关系数法优选出6个与SOH高度相关的健康因子作为模型的输入。然后,在当前常用的7个核函数集合上,通过两两随机组合构造新的组合核函数,并利用交叉验证自适应优选出最优组合核函数。采用3个不同数据集对所提方法进行了验证,结果表明:本文方法具有出色的SOH区间估计性能。在3个公开数据集上,平均区间宽度指标在0.0509以内,平均区间分数大于-0.0004,均方根误差小于0.0181。
文摘长春市是国家新型城镇化综合试点城市,识别长春市中心城区功能,针对当前存在的问题提出对策建议,对城市空间的优化与协调具有重要意义。以兴趣点(Point of Interest,POI)数据及开放街道地图(Open Street Map,OSM)数据为基础,结合核密度分析、实地调查验证等方法,识别长春市中心城区城市功能类型。结果表明:单一功能区中,商业功能区数量最多,居住功能区最少;主导—混合功能区中的商业主导功能区及交通主导功能区形成对商业聚集区与轨道交通系统的重要补充;细分—混合功能区特征显示功能混合程度从市中心向周边逐渐加大。经验证,城市功能识别结果符合长春市实际,由此提出对策建议:未来长春市中心城区应注重多中心发展格局,并加强绿地空间和公共服务设施建设。
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) .
