基于条件概率积分变换的多元Copula函数选择

本文构建了基于条件概率积分变换的Copula函数选择方法,通过对条件概率积分变换下Anderson-Darling(AD)、Kolmogorov-Smirnov(KS)、Cramér-von Mises(CM)这三种统计量的比较,讨论在不同样本容量和变量维数下其对多种Copula函数的拟合效果。利用GSPTSE、INMEX.MX和NDX三大股指样本,将基于条件概率积分变换的Copula函数选择方法与核密度估计和极大似然估计选择法的效果进行系统比较。结果表明,基于条件概率积分变换的检验法可以有效解决多元Copula函数的选择问题,其拟合优度检验更精确、更稳定;核密度估计检验在大样本下比较稳定,而小样本下稳定性较差;相比之下,极大似然值检验法则不稳定。     

分数布朗运动下带违约风险的可转换债券定价

应用均衡定价方法,考虑股票价格和公司资产价值服从分数布朗运动以及存在公司违约风险情况下的可转债定价问题;建立相应的可转债定价模型,采用拟鞅定价方法,得出了欧式看涨期权的显式解,进而得出了可转债定价公式;最后利用数值算例进行分析,结论表明公司违约风险、股票价格和公司资产价格的长程关联性是可转债定价时不可忽略的因素。     

Copula-based predictions in small area estimation

Unit-level regression models are commonly used in small area estimation (SAE) to obtain an empirical best linear unbiased prediction of small area characteristics. The underlying assumptions of these models, however, may be unrealistic in some applications. Previous work developed a copula-based SAE model where the empirical Kendall's tau was used to estimate the dependence between two units from the same area. In this article, we propose a likelihood framework to estimate the intra-class dependence of the multivariate exchangeable copula for the empirical best unbiased prediction (EBUP) of small area means. One appeal of the proposed approach lies in its accommodation of both parametric and semi-parametric estimation approaches. Under each estimation method, we further propose a bootstrap approach to obtain a nearly unbiased estimator of the mean squared prediction error of the EBUP of small area means. The performance of the proposed methods is evaluated through simulation studies and also by a real data application.     

Approximation to two independent Gaussian processes from a unique Lévy process and applications

Abstract

In this article, we construct two families of processes, from a unique Lévy process, the finite dimensional distributions of which converge in law towards the finite dimensional distributions of the two independent Gaussian processes. As applications of this result, we obtain families of processes that converge in law towards fractional Brownian motion, sub-fractional Brownian motion and bifractional Brownian motion, respectively.     

Non-parametric estimation of copula based mutual information

Abstract

Mutual information is a measure for investigating the dependence between two random variables. The copula based estimation of mutual information reduces the complexity because it is depend only on the copula density. We propose two estimators and discuss the asymptotic properties. To compare the performance of the estimators a simulation study is carried out. The methods are illustrated using real data sets.     

紧集上布朗单多重时的Hausdorff维数

讨论了紧集上布朗单多重时的Hausdorff维数 ,得到了几个结果     

A note on the residual median process

We study the residual median process, defined as the median of those observations which are greater than a number t. Using appropriate limit theorems, it is shown that the stochastic process converges in law to a Gaussian process defined in terms of a Brownian bridge.     

Devaluation expectations and the unit root hypothesis: The Italian Lira in the European monetary system

Summary In several studies the unit root hypothesis of EMS exchange rates is analysed within the context of devaluation expectations estimation. By means of bootstrap inference it is shown that these procedures are not compatible with standard Dickey-Fuller significance levels and may lead to a wrong rejection of the null hypothesis. In the case of the Italian Lira/Deutsche Mark exchange rate, the hypothesis of a unit root is not rejected and expectations can be modelled by means of a reflected Brownian motion. The estimated devaluation expectations are related with some macro variables which provide evidence for the structure of expectations. This research has been partially supported with 40% and 60% MURST grants. The author wishes to thank the Bank of Italy for the exchange rates and the interest rates data and Ulf S?derstr?m for providing macroeconomic indicators. Useful suggestions from Riccardo Cesari, Michele Costa and two anonymous referees are gratefully acknowledged.     

Uniform asymptotic linearity in a regression parameter of a process based on a rank statistic

For X₁, …, X_N a random sample from a distribution F, let the process S^δ_N(t) be defined as where K²_N = σ^N_i=1(c_i ? c?)² and R x_i, + Δd, is the rank of X_i + Δd_i, among X₁ + Δd₁, …, X_N + Δd_N. The purpose of this note is to prove that, under certain regularity conditions on F and on the constants c_i and d_i, S^Δ_N (t) is asymptotically approximately a linear function of Δ, uniformly in t and in Δ, |Δ| ≤ C. The special case of two samples is considered.