The Wiener Sequential Testing Problem with Finite Horizon

We present a solution of the Bayesian problem of sequential testing of two simple hypotheses about the mean value of an observed Wiener process on the time interval with finite horizon. The method of proof is based on reducing the initial optimal stopping problem to a parabolic free-boundary problem where the continuation region is determined by two continuous curved boundaries. By means of the change-of-variable formula containing the local time of a diffusion process on curves we show that the optimal boundaries can be characterized as a unique solution of the coupled system of two nonlinear integral equations.     

A martingale approach for detecting the drift of a Wiener process

Lerchez (Ann. Statist. 14, 1986b, 1030–1048) considered a sequential Bayes-test problem for the drift of the Wiener process. In the case of a normal prior an o(c)-optimal test could be constructed. In this paper a new martingale approach is presented, which provides an expansion of the Bayes risk for a one-sided SPRT. Relations to the optimal Bayes risk are given, which show the o(c)-optimality for suitable nonnormal priors.     

Testing Hypotheses About the Power Law Process Under Failure Truncation Using Intrinsic Bayes Factors

Conventional Bayes factors for hypotheses testing cannot typically accommodate the use of standard noninformative priors, as such priors are defined only up to arbitrary constants which affect the values of the Bayes factors. To circumvent this problem, Berger and Pericchi (1996, J. Amer. Statist. Assoc., 19, 109-122) introduced a new criterion called the Intrinsic Bayes Factor (IBF). In this paper, we use their methodology to test several hypotheses regarding the shape parameter of the power law process. Assuming that we have data from the process according to the failure-truncation sampling scheme, we derive the arithmetic and geometric IBF's using the reference priors. We deduce a set of intrinsic priors that correspond to these IBF's, as the observed number of failures tends to infinity. We then use these results to analyze an actual data set on the failures of an aircraft generator.     

基于维纳过程步进应力加速退化试验的客观贝叶斯分析

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.     

Wiener过程分布密度的矩阵算法

在随机过程的理论及其应用中．Ｗｉｅｎｅｒ过程起着基本的作用．本文结出用矩阵的初等变换，建立Ｗｉｅｎｅｒ过程ｐ．ｄ，ｆ的一个崭新的方法；此方法，对理解过程的统计特性，掌握过程的ｐ，ｄ，ｆ的结构等，均是有益的．     

N指标d维广义Wiener过程极集的性质

研究了Ｎ指标ｄ维广义Ｗｉｅｎｅｒ过程极集的性质,得到了其极性的必要条件．     

A note on the empty balls left by a critical branching Wiener process

Summary In this note, we partially confirm some conjectures of P. Révész [10] on the critical branching Wiener process.     

在R^d的VC类上Wiener测度的上界

本文考察指标集为d维欧氏空间Rd的子集类c的Wiener过程W的样本轨道性质．在某些情形中，对0＜an≤nd，an是不减的且an／nd是不增的假设下，求得函数Ψn使给出了Wiener测度在Rd的VC类的界，它也推广了Csorgo－Revesz关于Wiener过程增量的结果于这一一般情形．     

估计感度分布中位数的两阶段优化序贯试验设计方法研究

感度试验在爆炸科学领域有非常广泛的应用,其中位数是含能材料的一个关键性能指标.高效估计感度分布中位数是实际工程应用中的重要问题.文章提出一种两阶段的优化序贯试验设计方法来估计感度分布的中位数,并将正交设计与两阶段优化序贯试验设计方法相结合给出了筛选影响含能材料安定性重要因子的试验设计方法.广泛的模拟比较验证了所提方法在小样本情况下可以获得感度分布中位数的准确估计,并且对模型假设和初始参数猜测具有一定的稳健性.当因子效应不是太小的时候,因子筛选方法可以准确地筛选出有显著影响的因子.     

Sequential Estimation for a Functional of the Spectral Density of a Gaussian Stationary Process

Integral functional of the spectral density of stationary process is an important index in time series analysis. In this paper we consider the problem of sequential point and fixed-width confidence interval estimation of an integral functional of the spectral density for Gaussian stationary process. The proposed sequential point estimator is based on the integral functional replaced by the periodogram in place of the spectral density. Then it is shown to be asymptotically risk efficient as the cost per observation tends to zero. Next we provide a sequential interval estimator, which is asymptotically efficient as the width of the interval tends to zero. Finally some numerical studies will be given.     

广义n参数Wiener过程和广义OUPn的导出过程的注记

记为非负单增函数且一阶偏导数均存．本文证明：（ｉ）广义ｎ参数Ｗｉｅｎｅｒ过程（ＧＢｎ）和广义ｎ参数Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程（广义ＯＵＰｎ）在Ｄ中导出的过程是马氏过程；（ｉｉ）如果ＧＢｎ（或广义ＯＵＰｎ）在Ｄ中导出的过程成为某个ＧＢｋ（或某个广义ＯＵＰｋ），则ｆｊ（ｔ１…，ｔｋ）未必恒为正常数．（ｊ＝ｋ＋１，…，ｎ）．     

保费依赖向后重现时间过程风险模型的破产概率上界(英文)

本文研究带利率的风险模型,它的索赔计数过程是一个更新计数过程,保费收入依赖于向后重现时间过程.通过鞅方法和递推技术,得到破产概率的两个指数型上界.最后,还研究了几个具体的例子,并且给出上界的数量比较.     

Some test statistics based on the martingale term of the empirical distribution function

Summary It is proved that the martingale term of the empirical distribution function converges weakly to a Gaussian process inD[0, 1]. Some statistics for goodness-of-fit tests based on the martingale term of the empirical distribution function are proposed. Asymptotic distributions of these statistics under the null hypothesis are given. The approximate Bahadur efficiencies of the statistics to the Kolmogorov-Smirnov statistic and to the Cramér-von Mises statistic are also calculated. The Institute of Statistical Mathematics     

Testing the Gumbel Hypothesis Via the Pot-Method

We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.     

Bivariate Sign Tests Based on the Sup, L 1 and L 2 Norms

The bivariate location problem is considered. The sup, L ₁ and L ₂ norms are used to construct bivariate sign tests from the univariate sign statistics computed on the projected observations on all lines passing through the origin. The tests so obtained are affine-invariant and distribution-free under the null hypothesis. The sup-norm gives rise to Hodges' test. A class of tests derived from the L ₂-norm, with Blumen's test as a member, is seen to be related to a class proposed by Oja and Nyblom (1989, J. Amer. Statist. Assoc., 84, 249-259). The L ₁-norm gives rise to a new test. Its asymptotic null distribution is seen to be the same as that of the L ₁-norm of a certain normal process related to the standard Wiener process. An explicit expression of its cumulative distribution function is given. A simulation study will examine the merits of the three approaches.