非参数核密度估计与Copula

本文提出非参数核密度估计-ML方法来估计Copula函数中的未知参数;再由统计检验推断得到能较好描述金融资产之间非线性相关结构的Copula。实证分析表明:可以利用Clayton Copula、Gumbel Copula来描述A股市场上证指数与深证成指之间的非线性相关结构.     

基于R~d上核密度估计的对称检验的中偏差

设f_n是基于一个核函数K和取值于R~d的独立同分布随机变量列的一个非参数核密度估计.推广了何和高一文中相应中偏差的结果,即证明统计量sup_(x∈R)~d|f_n(x)-f_n(-x)|的中偏差,并给出了两个具体的模拟例子.     

基于R~d上核密度估计的对称检验的大偏差（英文）

设f_n是基于一个核函数K和取值于R~d的独立同分布随机变量列的一个非参数核密度估计.本文推广了在He和Gao(2008)中相应大偏差的结果,即证明统计量sup x∈Rd|f_n(x)-f_n(-x)|的大偏差.     

基于自助法和核密度估计的膳食暴露评估模型

针对现阶段我国食品卫生安全保障体系的不完善,建立了基于自助法和核密度估计的膳食暴露评估模型.首先给出一种食物摄入量的抽样调查方案,并按污染物含量对特征人群进行模糊区间分类,建立特征人群每人每天食物摄入量的截尾正态分布模型.然后通过自助法重复抽样,弥补偶然抽查数据数量上的不足,提出了用对数正态分布核密度来估计污染物分布,并对模型进行了检验.在此基础上,建立了污染物摄入量模型,利用Gauss-Legendre求积公式求出其99.999%的右分位点,并且采用模糊匹配技术解决了数据不配套问题.最后对模型进行了讨论,给出了一种思路.     

随机删失数据下核密度估计的Berry-Esseen界

本文在随机删失数据下研究了概率密度函数的核估计,获得了此核估计的一个Berry－Esseen界.     

基于方向数据的核密度估计的对称检验的大偏差

设$f_n$是基于核函数$K$和取值于$d$-维单位球面${\mathbb{S}}^{d-1}$的独立同分布随机变量列的非参数核密度估计. 我们证明了若核函数是有界变差函数, 随机变量的密度函数$f$是连续的和对称的, $\{\sup_{x\in {\mathbb{SS}}^{d-1}}|f_n(x)-f_n(-x)|,n\ge 1\}$的大偏差原理成立.     

基于核密度估计的我国城乡居民收人差距的测度研究

伴随我国经济持续快速增长,我国城乡居民收入差距问题不断凸显.依据中国健康和营养调查的微观调查数据,利用非参数核密度估计方法对我国城乡居民收入密度曲线进行估计和分析.研究发现:我国城乡居民收入整体在持续提高,大部分城乡居民分享到了经济快速增长的成果,但中低收入家庭仍然是主体;我国城乡居民收入分布变动与改革开放进程高度相关;城镇居民收入增长速度和向高收入水平流动的速度都要快于农村居民,城乡居民收入差距持续扩大.     

方向数据核密度估计强一致相合性的收敛速度

设 f_n 为基于核函数 K 和一列取值于d 维单位球面的独立同分布的随机变量上的非参数核密度估计. 该文通过经验过程的方法得到核密度估计强一致相合性的速度.     

随机加权法在密度估计中的应用

本文给出了概率密度函数的椭机加权估计，证明了承机加权分布与密度估计的标准化估计量的分布的逼近精度可达到ｏ（１／√ｎｈ），并且构造了Ｅｆｎ（ｘ）的置信区间，其中ｆｎ（ｘ）为密度函数的核估计，ｈ＝ｈｎ炒估计的窗宽。     

极值理论在高频数据中的VaR和CVaR风险价值研究

高频数据具有与低频数据明显不同的特征。本文引入广义帕雷托分布代替传统的正态分布等,精确描述金融高频数据收益的厚尾特征;并且计算高频数据下的VaR和CVaR,然后利用深成A指数据进行返回检验。两种返回检验方法的结果表明,极值理论方法可以比较精确地度量VaR和CVaR。     

Heat Kernel Estimates for Operators with Boundary Conditions

We prove Gaussian upper bounds for kernels associated with non – symmetric, non – autonomous second order parabolic operators of divergence form subject to various boundary conditions. The growth of the kernel in time is determined by theboundary conditions and the geometric properties of the domain. The theory gives a unified treatment for Dirichlet, Neumann and Robin boundary conditions, and the existence of a Gaussian type bound is essentially reduced to verifying some properties of the Hilbert space in the weak formulation of the problem.     

密度核估计的随机加权法

利用随机加权法的思想,找出概率密度函数估计的随机加权统计量,在适当的条件下证明随机加权分布逼近核估计误差分布的精度为     

Pointwise Improvement of Multivariate Kernel Density Estimates

Multivariate kernel density estimators are known to systematically deviate from the true value near critical points of the density surface. To overcome this difficulty a method based on Rao–Blackwell's theorem is proposed. Local corrections of kernel density estimators are achieved by conditioning these estimators with respect to locally sufficient statistics. The asymptotic as well as the small sample size behavior of the improved estimators are studied. Asymptotic bias and variance are investigated and weak and complete consistency are derived under mild hypothesis.     

NA样本下一般形式的密度估计

Campos和Dorea(2001)在独立同分布样本下讨论了一般形式的核密度估计,得到了与连续型密度和离散型密度类似的结果,并将他们作为特例.本文则在NA样本下给出了类似的结果.     

Universal Consistency of Local Polynomial Kernel Regression Estimates

Regression function estimation from independent and identically distributed data is considered. The L ₂ error with integration with respect to the design measure is used as an error criterion. It is shown that suitably defined local polynomial kernel estimates are weakly and strongly universally consistent, i.e., it is shown that the L ₂ errors of these estimates converge to zero almost surely and in L ₁ for all distributions.     

Strong Convergence Rates of Double Kernel Estimates of Conditional Desity Under Stationary Sequences

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In the situation of rho-mixing dependent sequences, this paper studied the mean square error and the optimal bandwidth of distribution kernel estimator nu_{p,h} of VaR. And the optimal bandwidth minimized the mean square error. The density function of Laplace distribution is used in the calculation of bandwidthand we adopt the method of interpolation to compute specific value of bandwidth in this paper. According to the numerical simulations, the distribution kernel estimator is more accurate by comparing the performance of VaR distribution kernel estimation with a common order statistic. Finally, Shangzheng A-share index and Shenzheng B-share index are chosen for an empirical research, which concludes that the risk of the latter is significantly higher than that of the former.     

基于非参数分布的沪深股市VaR测度

沪深大盘指数的收益率分布函数并不服从通常人们所认为的正态分布.因此,采用一种新的方法—非参数核密度估计,对沪深股指收益率分布进行拟合.该方法不仅很好地刻画了收益率分布的尖峰和肥尾特征,而且由此建立的VaR模型比一般的基于参数分布的VaR模型更能捕捉市场的风险特征,结论也更加准确.     

Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385–431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster. J. Misumi research partially supported by the 21 century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.