非参数核密度估计在恒生指数收益率分布中的应用

文章采用了一种新的方法--非参数核密度估计,对恒生大盘指数的收益率分布函数进行了研究.这种新方法不仅很好地刻画了收益率分布的尖峰肥尾等非线性特征,而且比一般的正态分布更能捕捉市场的风险特征,结论也更加准确.     

财产保险中损失分布建模的方法性研究

一、引言在财产保险中 ,保费计价、损失理赔是保险业务的核心问题 ,而保费的定价首先必须知道所考虑险种的损失分布。从大的保险范畴划分来看可以分为两类 :一类是寿险 ,另一类是非寿险。财产保险属于非寿险范畴 ,该险种不同于寿险的保费计价相对简单。因为寿命周期表提供了很大的帮助 ,各寿险公司均可参考利用。但是 ,财产保险就不同了 ,不同的保险标的 ,不同的灾情因素所服从的具体分布是不同的 ,即便是能够判断出所服从的损失分布其参数的确定也是相当困难的 ,有时同一个险种 ,同一个灾情因素随着时间和环境的变化其损失分布也在发生着不…     

Copula函数的非参数核密度估计

Copula函数包含了变量的边际分布和变量间的相关结构两方面的信息.用Copula函数可以很灵活地构造相关结构和边际分布不同的联合分布函数.Archimedean Copula函数在金融市场分析中很有用.在用Copula理论建模的过程中有一个很重要的环节是参数估计.文章采用对边际分布不作具体假设的非参数核密度方法来估计Archimedean Copula的参数,并用实证说明方法的有效性.     

非参数随机条件持续期模型及其迭代算法

 随机条件持续期（SCD）模型能有效刻画超高频时间序列中持续期的变化,但该模型假定期望持续期生成机制固定,且模型参数估计存在一定的困难。文章在不假定条件均值形式和冲击项分布的基础上结合核估计方法提出了非参数SCD模型及其迭代求解方法。然后,基于TEACD(1,1)模型生成的模拟数据,将非参数SCD模型与用卡尔漫滤波进行伪似然估计的参数SCD模型和用Gibbs抽样进行马尔科夫蒙特卡罗估计的参数SCD模型的拟合效果进行比较,实证表明在大样本条件下非参数SCD模型的拟合效果与用MCMC估计的参数SCD模型的拟合结果相差不大,但明显优于用QML估计的参数SCD模型的拟合结果,且非参数SCD模型能为参数SCD模型的参数设定提供参考。     

基于GARCH和半参数法的VAR模型及其在中国股市风险中的应用

This article introduces value at risks model(VAR) based on GARCH and semi-parameter approach, a new recently developed tool for measuring market risks. And we also made a case analysis on Chinese Stock Market Risk using this technique.     

自适应滤波在经济预测中的应用

自适应滤波在经济预测中的应用高健绪,顾岚一、自适应滤波及预测方法设｛Ｘｔ｝（ｔ＝１,２,．．．,Ｎ）是一个实际观测到的经济序列,不失一般性,可以认为它具有趋势性和季节性,我们可用长自回归模型ＡＲ（ｎ）对其进行拟合。式（１）中误差项｛εｔ｝是零均值白噪...     

回归模式在农产量预测中的应用

为了满足我国四化建设和安排人民生活的需要,要求及时提供准确的农产量资料。国家统计局现行的农产量多阶段等距随机抽样调查就是适应这种要求的一个措施。但是这个调查只能提供农作物实割实测时的产量资料,还不能满足早期国家决策和各级政府指导生产的需要。因此有必要在已有抽样点的基础上利用各种方法对农产量进行早期预测。回归模式就是在这种情况下提出来的一种预测方法。     

固定样本在经济统计分析中的应用

理论、方法和数据是经济统计分析赖以成功的三个基本要素。其中数据反映研究对象的活动水平、相互间的关系以及外部环境 ,是人们认识经济现象的基本依据 ,也是经济统计分析的原料。由于数据直接影响研究的结果 ,因此保证数据的质量是十分必要的。实践证明 ,要想获得高质量的数据 ,必须在经济理论和统计理论的指导下选择数据模型和收集数据 ,二者缺一不可。然而 ,实际研究中人们往往对数据的统计特性比较重视 ,而对于数据是否准确地反映它所描述的经济因素的状态缺乏细致地考察。即调查数据本身是客观、准确的 ,但是并不能满足建立经济模型的…     

营养研究在住户调查中的应用

住户调查是统计部门对人民生活进行的经常性调查。对住户调查从不同的方面去研究和剖析,能够观察和衡量人民生活的现状。特别是分析摄取营养成份的数量,能够了解人民生活水平的高低和差异程度并可在不同地区、不同国家之间进行比较,从而为研究贫困问题,指导人们合理的膳食提供科学的依据。对食品营养成份的研究有专门的机构,如食品与卫生研究所,这些机构有专门的设备和人员,他们测定各种食品营养成份的含量,并对营养与人体健康进行全面的分析。他们也进     

Bootstrap方法在复杂抽样中的应用

一、Bootstrap方法简介Bootstrap方法是美国统计学家Bradley·Efron在1979年提出的一种处理非参数统计推断问题的方法。它的一般提法是:已知来自总体(Y,(?),F)的简单随机样本Y_n=(y_1,y_2,…,Y_n),其中F是一未知的分布函数。设R(Y_n,F)是我们感兴趣的样本函数,我们欲得到R(Y_n,f)的某些信息,如:R(Y_n,F)的分布函数、E_FR、Var_FR或P_F(R<2)等等;下标F表示在分布函数F下求期望、方差或概率。所谓Bootstrap方法,就是用样本Y_n构造出F的极大似然估计(?)_n(一般就用样本Y_n的经验分布函数F_n来近似);然后,从F_n中抽出大小为n的简单随机样本Y_n~*=(Y_1~*,Y_2~*,     

Deconvolution boundary kernel method in nonparametric density estimation

This paper considers the nonparametric deconvolution problem when the true density function is left (or right) truncated. We propose to remove the boundary effect of the conventional deconvolution density estimator by using a special class of kernels: the deconvolution boundary kernels. Methods for constructing such kernels are provided. The mean squared error properties, including the rates of convergence, are investigated for supersmooth and ordinary smooth errors. Numerical simulations show that the deconvolution boundary kernel estimator successfully removes the boundary effects of the conventional deconvolution density estimator.     

Variable kernel density estimation

This paper considers the problem of selecting optimal bandwidths for variable (sample‐point adaptive) kernel density estimation. A data‐driven variable bandwidth selector is proposed, based on the idea of approximating the log‐bandwidth function by a cubic spline. This cubic spline is optimized with respect to a cross‐validation criterion. The proposed method can be interpreted as a selector for either integrated squared error (ISE) or mean integrated squared error (MISE) optimal bandwidths. This leads to reflection upon some of the differences between ISE and MISE as error criteria for variable kernel estimation. Results from simulation studies indicate that the proposed method outperforms a fixed kernel estimator (in terms of ISE) when the target density has a combination of sharp modes and regions of smooth undulation. Moreover, some detailed data analyses suggest that the gains in ISE may understate the improvements in visual appeal obtained using the proposed variable kernel estimator. These numerical studies also show that the proposed estimator outperforms existing variable kernel density estimators implemented using piecewise constant bandwidth functions.     

Shape constrained kernel density estimation

In this paper, a method for estimating monotone, convex and log-concave densities is proposed. The estimation procedure consists of an unconstrained kernel estimator which is modified in a second step with respect to the desired shape constraint by using monotone rearrangements. It is shown that the resulting estimate is a density itself and shares the asymptotic properties of the unconstrained estimate. A short simulation study shows the finite sample behavior.     

On kernel density derivative estimation

Estimators of derivatives of a density function based on polynomial multiples of kernels are compared with those based on differentiated kernels.     

Weighted log-normal kernel density estimation

ABSTRACT

The log-normal (LN) kernel estimator of a density with support [0, ∞) was discussed by Jin and Kawczak (2003 Jin, X., Kawczak, J. (2003). Birnbaum–Saunders and lognormal kernel estimators for modelling durations in high frequency financial data. Ann. Econ. Finance 4:103–124. [Google Scholar]). The contribution of this paper is to suggest a new class of LN kernel estimators using the idea of weighted distribution. The asymptotic properties of the new class of estimators are studied. Also, numerical studies based on both simulated and real data set are presented.     

A generalized reflection method of boundary correction in kernel density estimation

The kernel method of estimation of curves is now popular and widely used in statistical applications. Kernel estimators suffer from boundary effects, however, when the support of the function to be estimated has finite endpoints. Several solutions to this problem have already been proposed. Here the authors develop a new method of boundary correction for kernel density estimation. Their technique is a kind of generalized reflection involving transformed data. It generates a class of boundary corrected estimators having desirable properties such as local smoothness and nonnegativity. Simulations show that the proposed method performs quite well when compared with the existing methods for almost all shapes of densities. The authors present the theory behind this new methodology, and they determine the bias and variance of their estimators.     

Bias reduction in kernel density estimation

In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, ‘The stochastic approximation method for the estimation of a multivariate probability density’, J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.     

PROMETHEE IV through kernel density estimation

ABSTRACT

This paper presents a new version of PROMETHEE IV, which considers the empirical distribution of the criteria through kernel density estimation to evaluate alternatives. The developed method has the ability to treat criteria according to their distribution. The classic PROMETHEE IV can produce divergent integrals, and this could be the cause for its insufficient exploration in literature. The proposed method overcomes this situation since large values have little weight compared to values near the mean.     

Using pseudometrics in kernel density estimation

Common kernel density estimators (KDE) are generalised, which involve that assumptions on the kernel of the distribution can be given. Instead of using metrics as input to the kernels, the new estimators use parameterisable pseudometrics. In general, the volumes of the balls in pseudometric spaces are dependent on both the radius and the location of the centre. To enable constant smoothing, the volumes of the balls need to be calculated and analytical expressions are preferred for computational reasons. Two suitable parametric families of pseudometrics are identified. One of them has common KDE as special cases. In a few experiments, the proposed estimators show increased statistical power when proper assumptions are made. As a consequence, this paper describes an approach, where partial knowledge about the distribution can be used effectively. Furthermore, it is suggested that the new estimators are adequate for statistical learning algorithms such as regression and classification.