Non-parametric recursive estimates of a probability density function and its derivatives

Recursive estimates of a probability density function (pdf) are known. This paper presents recursive estimates of a derivative of any desired order of a pdf. Let f be a pdf on the real line and p?0 be any desired integer. Based on a random sample of size n from f, estimators f^(p)_n of f^(p), the pth order derivatives of f, are exhibited. These estimators are of the form $\text{n}{}^{\mathrm{?1}}\text{∑n}\text{j=1}\text{δ}{}_{\mathrm{jp}}$, where δ_jp depends only on p and the jth observation in the sample, and hence can be computed recursively as the sample size increases. These estimators are shown to be asymptotically unbiased, mean square consistent and strongly consistent, both at a point and uniformly on the real line. For pointwise properties, the conditions on f^(p) have been weakened with a little stronger assumption on the kernel function.     

On Wavelet Estimation of the Derivatives of a Density Based on Biased Data

Here, we consider wavelet based estimation of the derivatives of a probability density function under random sampling from a weighted distribution and extend the results regarding the asymptotic convergence rates under the i.i.d. setup studied in Prakasa Rao (1996 Rao, B. L.S. (1996). Nonparametric estimation of the derivatives of a density by the method of wavelets. Bull. Inform. Cybernat. 28:91–100. [Google Scholar]) to the biased-data setup. We compare the performance of the wavelet based estimator with that of the kernel based estimator obtained by differentiating the Efromovich (2004 Efromovich, S. (2004). Density estimation for biased data. Ann. Statist. 32:1137–1161.[Crossref], [Web of Science ®] , [Google Scholar]) kernel density estimator through a simulation study.     

中国金融市场的风险构成及其应对策略

经济体制模式和金融体系的开放程度会在基本面上决定一国的金融市场风险构成,不同的市场风险构成会引导政府对金融危机有不同的应对措施.针对有可能再次发生的国际金融危机,如何在理论上概要地梳理出中国金融市场的风险构成,如何依据这些构成来解析国际金融危机对中国发生的冲击及如何应对金融危机,这些问题的研究,要求我们在理论上考察中国现存的各种制度安排与现实的关联,要求我们结合体制模式或制度安排来寻找应对金融危机的方法和途径.国际金融危机在许多领域对中国产生冲击的事实,在规定着政府必须依据现实做出战略决策和手段选择的同时,也对经济理论研究提出了新的任务和要求.本文的分析可视为对这些任务和要求的一种学术讨论.     

欧式热率相关期权的定价

本文将含有电力的市场视为电力无法交易的不完全市场,利用Davis不完全市场定价理论给出了欧式热率相关期权的定价公式。在特殊电力价格模型下,得到了期权价格的解析解。     

二茂铁衍生物的生物活性

本文针对二茂铁衍生物在生物学、医学、微生物等方面的应用进行了简要综述．     

信用衍生品的法律规制:国际改革趋向及启示

信用衍生品对于提高金融机构的风险管理水平和整个金融体系的安全和效率都具有重要作用。但是,由于缺乏有效的法律规制,信用衍生品逐渐由风险管理工具转变为投机工具。危机后,全球范围内的场外金融衍生品规制框架重构渐次展开。对于信用衍生品法律规制的主要内容,可以归纳为集中清算、信用风险管理和信息透明化三个方面。这些国际改革实践,对我国信用衍生品市场及其法制的构建和发展具有重要的借鉴意义。     

金融监管模式的变革及资本市场统合法的诞生——以金融衍生产品监管为视角

金融衍生产品和混业经营的发展对以金融组织机构性质为标准而形成的传统金融监管模式提出挑战.旨在有效解决金融业混业经营格局下金融创新产品的监管归属问题,避免监管"真空"和多重监管,依功能性监管规则而形成的统一金融监管模式及制定资本市场统合法的金融法改革方兴未艾.我国应积极应对"金融监管现代化"的全球趋势,尽快构建起适合中国国情的和谐生态的金融监管体制,在金融衍生产品的监管上,建立和完善牵头监管模式.     

A comparative study of some bias correction techniques for kernel- based density estimators

Methods for obtaining kernel-based density estimators with lower bias and mean integrated squared error than an estimator based on a standard Normal kernel function are described and discussed. Three main approaches are considered which are: firstly by using 'optimal' polynomial kernels as described, for example, by Gasser er a1 (1985); secondly by employing generalised jackknifing as proposed by Jones nd Foster (1993) and thirdly by subtracting an estimator of the principal asymptotic bias term from the original estimator. The emphasis in this initial discussion is on their asymptotic properties. The finite sample performance of those that have the best asymptotic properties are compared with two adaptive estimators, as well as the fixed Normal kernel estimator, in a simulation study.