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几何分布时间序贯检验的贝叶斯推断 总被引:13,自引:1,他引:12
设有统计模型{x,Bx,Pθ},θ∈(0,1),其中Pθ为几何分布:Pθ(X=k)=(1-θ)θ^k-1k=1,2,…。考虑检验问题:θ=θo vs. θ=θ1(0〈θ0〈θ1〈1)本文对一种依次试验的时间序贯样本,给出了上述检验问题的贝叶斯停止判决法则,其中损失函数为试验费用和误判损失之和,贝叶斯停止判决法则由后验概率的两组界(上界和下界)所给出。 相似文献
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本文研究零假设为复杂情况时的P值问题。对于一维正态均值的单边检验H_0:θ≤θ_0,P值是指拒绝域在参数θ=θ_0时的概率。根据这一想法,本文定义了一般情况下的边界P值。当零假设是一个多面体凸锥时,本文给出了一个计算边界P值的方法,并利用这个方法解决了一个实际问题。 相似文献
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关于经验 Bayes 检验的研究,目前在文献上能见到一些结果,其中部分是讨论经验Bayes 检验的渐近最优性及其收敛速度,参见[1—4,6,7,9];最近 stijnen 讨论了连续型单参数指数族中经验 Bayes 检验的条件 Bayes 风险的渐近分布,从而得到了精确的收敛速度.本文我们将讨论均匀分布族{U(0,θ),θ>0)中经验 Bayes 检验的条件 Bayes 风险的极限分布,从而得到了经验 Bayes 检验的渐近最优性及其收敛速度. 相似文献
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本文研究如下线性自排斥扩散过程的参数估计问题:X_t~H=B_t~H+θ∫_0~t∫_0~θ(X_B~H-X_u~H)dudθ+vt其中X_O~H=0,B~H是Hurst指数为1/2≤H1的分数Brown运动,且θ0和υ∈R是两个未知参数.该过程为一类自交互扩散过程的类似过程.在连续观测条件下,本文利用最小二乘法给出这两个参数的估计,并且讨论了它们的相合性和渐近分布. 相似文献
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本文,我们把递归算术系统简化为下列三个系统:A_0V_2、A_0V_1I_2θ_2及A_0V_1I_2θ_2~*,此处A_0为存在性公理,而V_n、I_n、θ_n、θ_n~*为唯一性规则,其定义如下:A_0是:给了H(x,y),存在一函数F(u,x),使得规则V_n是:此处是指“可推导出”,x为约束变元,它在前件中不能进行代入,I_n是V_n当H是么函数I(I(x)=x)时的特例,θ_n是V_n当H为θ(θ(x)=0)时的特例,θ_n~*又是θ_n当F(u_1,…,u_n,0)=0时的特例。 相似文献
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本文主要研究在参数θ>0和Hurst指数H∈(1/2,1)的情形下第二类分数布朗桥的最小二乘估计.使用Malliavin分析方法获得了估计量的一致收敛性和近似分布. 相似文献
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本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性. 相似文献
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本文考虑一维双边截断型分布族参数函数在平方损失下的经验 Bayes估计问题 .给定θ,X的条件分布为f (x|θ) =ω(θ1,θ2 ) h(x) I[θ1,θ2 ] (x) dx其中θ =(θ1,θ2 )T(x) =(t1(x) ,t2 (x) ) =(min(x1,… ,xm) ,max(x1,… ,xm) )是充分统计量 ,其边缘密度为 f (t) ,本文通过 f (t)的核估计构造出θ的函数的经验 Bayes估计 ,并证明在一定的条件下是渐近最优的 (a.0 .) 相似文献
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Suppose that for i = 1,2, a Bernoulli random variable with success probability θi is observable from population i. The problem is to estimate θ = θ1θ2 using a Bayesian approach with squared error estimation loss in θ. For estimating θ, the best nonrandom sampling scheme, the two-stage sampling scheme, and the optimal sampling scheme are discussed. It is shown that the two-stage sampling scheme is typically asymptotically optimal, and can improve the Bayes risk (over the best nonrandom allocation) up to fifty percent 相似文献
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TaChen Liang 《Journal of Applied Mathematics and Computing》2010,32(1):97-109
This paper studies a monotone empirical Bayes test δ n * for testing H 0:θ≤θ 0 against H 1:θ>θ 0 for the positive exponential family f(x|θ)=c(θ)u(x)exp?(?x/θ), x>0, using a weighted quadratic error loss. We investigate the convergence rate of the empirical Bayes test δ n * . It is shown that the regret of δ n * converges to zero at a rate O(n ?1), where n is the number of past data available when the present testing problem is considered. Errors regarding the rate of convergence claimed in Gupta and Li (J. Stat. Plan. Inference, 129: 3–18, 2005) are addressed. 相似文献
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Let ∏1,…,∏k denote k independent populations, where a random observation from population ∏ i has a uniform distribution over the interval (0,θ i ) and θ i is a realization of a random variable having an unknown prior distribution G i . Population ∏ i is said to be a good population if θ i ≥θ0, where θ0 is a given, positive number. This paper provides a sequence of empirical Bayes procedures for selecting the good populationsamong ∏1,…,∏ k . It is shown that these procedures are asymptotically optimal and that the order of associated convergence rates is O(n-r/4) for some r, 0<r<2, where n is the number of accumulated past observations at hand 相似文献
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Tachen Liang 《Journal of Applied Mathematics and Computing》2007,25(1-2):1-15
Consider a Rayleigh distribution withpdfp(x|θ) = 2xθ - 1 exp(- x 2/θ) and mean lifetime μ = √πθ/2. We study the two-action problem of testing the hypothesesH 0: μ≤ μ0 againstH 1: μ > μ0 using a linear error loss of |μ- μ 0 | via the empirical Bayes approach. We construct a monotone empirical Bayes test δ n * and study its associated asymptotic optimality. It is shown that the regret of δ n * converges to zero at a rate $\frac{{\ln ^2 n}}{n}$ , wheren is the number of past data available when the present testing problem is considered. 相似文献
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本文研究随机微分方程单支theta方法的均方稳定性.首先,对线性检验方程,当0≤θ<1时,分步单支theta方法在一定的步长限制下能保持原系统的均方稳定性,当θ=1时,方法按任意步长都能保持原系统的稳定性.其次,对满足单边Lipschitz条件的非线性随机微分方程,当1/2<θ0<θ<1时,方法能保持原系统的均方指数稳定性,但对步长有限制,如果θ=1,对步长限制消失. 相似文献
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在由信息论中的熵演绎出的一种新损失一加权P,q对称熵损失L(θ,δ)=θ/Pδp+δq/qθq-2(ρ,q>0)下,研究了一类指数分布模型c(x,η)θ-νe-νe-T(x)/θ的参数θ的Bayes估计的一般形式与精确形式,讨论了参数θ的形如cT(X)+d的一类估计的可容许性与不可容许性,并应用积分变换定理证明了参数θ的Bayes估计与可容许估计具有不变性, 相似文献
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Tachen Liang 《Journal of Applied Mathematics and Computing》2007,23(1-2):153-165
This paper deals with the empirical Bayes two-action problem of testingH 0 : θ ≤ θo versusH 1 : θ > θo using a linear error loss for some discrete nonexponential families having probability function either $\begin{gathered} f_1 (x|\theta ) = (x\alpha + 1 - \theta )\theta ^x /\prod\limits_{j = 0}^x {(j\alpha + 1)} \\ or \\ f_1 (x|\theta ) = \left[ {\theta \prod\limits_{j = 0}^{x - 1} {(j\alpha + 1 - \theta )} } \right]/\left[ {\prod\limits_{j = 0}^x {(j\alpha + 1)} } \right] \\ \end{gathered} $ Two empirical Bayes tests δn* and δn** are constructed. We have shown that both δn* and δn** are asymptotically optimal, and their regrets converge to zero at an exponential decay rate O(exp( -cn)) for some c > 0, wheren is the number of historical data available when the present decision problem is considered. 相似文献