操作风险计量研究——基于贝叶斯Copula方法

商业银行操作风险的计量存在两个重要的问题,一个问题是损失数据缺乏,另一个问题是各部分之间的风险相关问题.结合Bayes估计和Copula函数解决了上述两个问题并基于中国商业银行操作风险的损失数据对对操作风险的计量进行了实证分析.实证分析的结果表明无论考虑风险相关与否,基于极大似然估计的VaR与基于Bayes估计的VaR具有一定的差距.     

定数截尾两参数指数——威布尔分布形状参数的Bayes估计

在不同的损失函数下,本文研究了两参数指数—威布尔分布(EWD)形状参数的Bayes估计问题.基于定数截尾试验,当其中一个形状参数α已知时,给出了另一个形状参数θ在三种不同损失函数下的Bayes估计表达式,并求得了可靠度函数的Bayes点估计.最后运用随机模拟方法,将Bayes估计和极大似然估计进行了比较.结果表明,LINEX损失下Bayes估计的精度比极大似然估计高.     

多重Ⅱ型删失数据的近似似然函数及应用

多重Ⅱ型删失数据是一种很常见的数据删失类型，处理起来也非常困难，本文获得了多重Ⅱ型删失数据的一种近似似然函数，并证明了在大样本场合下，这种近似与似然函数是等价的。基于该近似似然函数，求得了参数的近似极大似然估计与近似Bayes估计，并讨论似极大似然估计的性质。     

对称熵损失下成功概率p的E-Bayes估计

研究对称熵损失下成功概率p的Bayes估计和E-Bayes估计,证明了前者的存在性及唯一性.模拟结果表明E-Bayes估计优于极大似然估计和Bayes估计.并将E-Bayes方法应用在证券投资预测之中,预测效果较好.     

双参数指数分布环境因子的Bayes估计

讨论了定数截尾样本下双参数指数分布环境因子的极大似然估计、区间估计和Bayes估计.以参数后验密度的商密度作为环境因子的后验密度,并结合专家经验运用Bayes方法给出了环境因子在平方损失下和LINEX损失下的Bayes估计.最后运用Monte Carlo方法对各估计结果的均方误差(MSE),进行了模拟比较.结果表明LINEX损失下环境因子的估计较好.     

AR(p)模型中的变点分析

本文分别用极大似然法和Bayes方法研究了AR(p)模型中的变点问题.在数据矩阵不一定满秩的条件下,利用Moore-Penrose广义逆给出了模型参数的极大似然估计的统一表达式和变点位置的估计式.在假定自回归系数的先验分布服从多元正态,方差服从逆Γ分布的条件下,用Bayes方法给出了变点位置估计的显示表达式以及模型参数的Bayes估计.     

敏感问题调查设计以及估计

对于多项选择敏感问题抽样调查,为了避开以往使用随机化调查时使用随机化装置带来的不便,提出一种间接问卷调查策略.结合问卷设计对个体隐私的保护度,对辅助信息的选择提出了的建议,并得到了敏感属性比例的极大似然估计和Bayes估计.数据模拟的结果显示,相比于极大似然估计,小样本时Bayes估计便有较高的精度.随着样本量的增加,两种估计结果趋于一致.提出的间接问卷调查策略,相比于以往的随机化调查技术,具有方便、省时等特点,可在实践中应用.     

对称熵损失下成功概率P的E—Bayes估计

研究对称熵损失下成功概率P的Bayes估计和E—Bayes估计,证明了前者的存在性及唯一性．模拟结果表明E-Bayes估计优于极大似然估计和Bayes估计．并将E—Bayes方法应用在证券投资预测之中,预测效果较好．     

基于Weibull寿命模型对工业中可靠度指标进行Bayes估计

主要研究了工业中可靠性指标R=P(Y X)的参数估计问题,其中X和Y是具有相同尺度参数但不同形状参数的Weibull分布的独立随机变量,计算得到了R的极大似然估计和近似的极大似然估计.进一步根据上述结果计算得到了相应的渐近分布,并用它来构造渐近的置信区间.同时考虑了非参数的Bootstrap置信区间.另外,提出了基于不同的Gibbs抽样方法的Bayes估计:Metropolis-Hastings和Adaptive Rejection Metropolis Sampling.最后,通过数值模拟和实际数据的分析来对比不同参数估计方法的性能.     

不完全信息下Ⅱ型截尾Weibull分布参数的极大似然估计及贝叶斯估计

给出了不完全信息下Ⅱ型截尾weibull分布参数的极大似然估计、无信息先验Bayes估计及多层Bayes估计,并指出针对一些具体模型还可以通过随机模拟来比较其估计精度.     

Boolean regression

We take a regression-based approach to the problem of induction, which is the problem of inferring general rules from specific instances. Whereas traditional regression analysis fits a numerical formula to data, we fit a logical formula to boolean data. We can, for instance, construct an expert system for fitting rules to an expert's observed behavior. A regression-based approach has the advantage of providing tests of statistical significance as well as other tools of regression analysis. Our approach can be extended to nonboolean discrete data, and we argue that it is better suited to rule construction than logit and other types of categorical data analysis. We find maximum likelihood and bayesian estimates of a best-fitting boolean function or formula and show that bayesian estimates are more appropriate. We also derive confidence and significance levels. We show that finding the best-fitting logical formula is a pseudo-boolean optimization problem, and finding the best-fitting monotone function is a network flow problem.The first and second authors gratefully acknowledge the partial support of NSF (Grant DMS 89-06870) and AFOSR (Grants 89-0512 and 90-0008), and the third author that of AFOSR (Grant 91-0287) and ONR (Grant N00014-92-J-1028).     

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??Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.     

Maximum Likelihood Estimation of Hidden Markov Multivariate Normal Distribution Parameters

Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.     

有关顺序统计量的极大似然估计

讨论了一类参数空间受样本限制的极大似然估计问题.分析了随机变量分布的非零区域与似然函数定义域的对应关系,提出如果分布的非零区域受参数限制,则无论似然方程是否可解,参数的极大似然估计必然与样本顺序统计量X_((n))或X_((1))有关,并具体分析了似然估计一定等于、一定不等于和可能等于顺序统计量X_((n))(X_((1)))的三种情形,并给出了相应的判别条件.最后分析得出在第三种判别条件之下,似然估计是否取值于x_((n))(x_((1)))视具体的样本观测值决定.     

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??In this paper, we concern with the estimation problem for the Pareto distribution based on progressive Type-II interval censoring with random removals. We discuss the maximum likelihood estimation of the model parameters. Then, we show the consistency and asymptotic normality of maximum likelihood estimators based on progressive Type-II interval censored sample.     

单参数Pareto分布变点估计研究

研究单参数Pareto分布存在变点时的估计问题,分别利用极大似然估计法和贝叶斯方法对单参数Pareto分布的变点进行估计,并运用Matlab软件进行随机模拟,随机结果表明贝叶斯方法与极大似然估计相比,估计值更接近真值.     

威布尔分布组与删失数据下最大似然估计的存在性

本文研究寿命服从威布尔分布,观测数据分组与可能删失的情况下,最大似然估计的存在性,针对所有数据类型,我们给出了最大似然估计存在性的一个充分必要条件,文章结尾讨论了仅一个失效数据时最大似然估计的计算。     

Asymptotic efficiency of the two-stage estimation method for copula-based models

For multivariate copula-based models for which maximum likelihood is computationally difficult, a two-stage estimation procedure has been proposed previously; the first stage involves maximum likelihood from univariate margins, and the second stage involves maximum likelihood of the dependence parameters with the univariate parameters held fixed from the first stage. Using the theory of inference functions, a partitioned matrix in a form amenable to analysis is obtained for the asymptotic covariance matrix of the two-stage estimator. The asymptotic relative efficiency of the two-stage estimation procedure compared with maximum likelihood estimation is studied. Analysis of the limiting cases of the independence copula and Fréchet upper bound help to determine common patterns in the efficiency as the dependence in the model increases. For the Fréchet upper bound, the two-stage estimation procedure can sometimes be equivalent to maximum likelihood estimation for the univariate parameters. Numerical results are shown for some models, including multivariate ordinal probit and bivariate extreme value distributions, to indicate the typical level of asymptotic efficiency for discrete and continuous data.     

Parameter estimation in nonlinear stochastic differential equations

We discuss the problem of parameter estimation in nonlinear stochastic differential equations (SDEs) based on sampled time series. A central message from the theory of integrating SDEs is that there exist in general two time scales, i.e. that of integrating these equations and that of sampling. We argue that therefore, maximum likelihood estimation is computationally extremely expensive. We discuss the relation between maximum likelihood and quasi maximum likelihood estimation. In a simulation study, we compare the quasi maximum likelihood method with an approach for parameter estimation in nonlinear SDEs that disregards the existence of the two time scales.