一重尾分布卷积的渐近表达式

本文主要研究了 Fn,* ∈ 时 W* F e(x,x+ z]的一渐近表达式 ,F ,W均为分布函数 .

企业信息不完全情况下的首次通过违约概率模型

基于Merton的结构化模型,利用几何布朗运动理论建立了不完全信息条件下的企业首次通过违约概率模型.根据企业的财务报表及信用记录,提出了一种新的不完全信息假设;在模型上引入股票的流通性价值,并改进其基于Merton模型的度量方法,使其适用于首次通过模型并求得内生违约边界,利用此边界给出了不完全信息条件下的企业违约概率,并分析了股票流通价值和股价与企业资产的相关关系对违约概率的影响.

On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

In this paper,we explore some weakly consistent properties of quasi-maximum likelihood estimates(QMLE) concerning the quasi-likelihood equation in=1 Xi(yi-μ(Xiβ)) = 0 for univariate generalized linear model E(y |X) = μ(X'β).Given uncorrelated residuals {ei = Yi-μ(Xiβ0),1 i n} and other conditions,we prove that βn-β0 = Op(λn-1/2) holds,where βn is a root of the above equation,β0 is the true value of parameter β and λn denotes the smallest eigenvalue of the matrix Sn = ni=1 XiXi.We also show that the convergence rate above is sharp,provided independent non-asymptotically degenerate residual sequence and other conditions.Moreover,paralleling to the elegant result of Drygas(1976) for classical linear regression models,we point out that the necessary condition guaranteeing the weak consistency of QMLE is Sn-1→ 0,as the sample size n →∞.

On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades,much attention has been paid to the two-sample Behrens-Fisher(BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures.Little work,however,has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures.In this paper we study this challenging problem via extending the famous Scheffe's transformation method,which reduces the k-sample BF problem to a one-sample problem.The induced one-sample problem can be easily tested by the classical Hotelling's T 2 test when the size of the resulting sample is very large relative to its dimensionality.For high dimensional data,however,the dimensionality of the resulting sample is often very large,and even much larger than its sample size,which makes the classical Hotelling's T 2 test not powerful or not even well defined.To overcome this diffculty,we propose and study an L2-norm based test.The asymp-totic powers of the proposed L2-norm based test and Hotelling's T 2 test are derived and theoretically compared.Methods for implementing the L2-norm based test are described.Simulation studies are conducted to compare the L2-norm based test and Hotelling's T 2 test when the latter can be well defined,and to compare the proposed implementation methods for the L2-norm based test otherwise.The methodologies are motivated and illustrated by a real data example.

The Gaussian approximation for multi-color generalized Friedman’s urn model

The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of a stochastic differential equation.This Gaussian approximation is important for the understanding of the behavior of the urn process and is also useful for statistical inferences.As an application,we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case.

Asymptotic distributions of non-central studentized statistics

Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applications to the power of the studentized U-and L-tests are also discussed.