Approximate Identifiability, Moments and Censored Data

It is well known that the joint distribution of a pair of random variables ( X,Y ) is not identifiable on the basis of the joint distribution of the function (min ( X,Y ), 1[ X < Y ]). This paper introduces the concept of approximate identifiability and studies its relevance to the function (min ( X,Y ), Y ). It shows that the distribution of ( X,Y ) is approximately identifiable on the basis of the distribution of (min ( X,Y ), Y ). The identification is explicitly executed by a method of moments. The method is applied to the analysis of censored distributions arising in the theory of clinical trials and is compared to the standard method of Kaplan and Meier.     

Estimating a covariance function having an un unknown scale kakameter

The structure of a family ρ of measures corresponding to a zero-mean Gaussian process with covariance αR(s,t) is discussed. When R itself is known (R and T completely arbitrary), it is shown that ρ is either homogeneous or composed of singular measures, depending on whether the reproducing kernel Hilbert space H(R,T) is finite- or infinite-dimensional. For the case dim H < ∞ the MLE α is given; when dim H = ∞ an almost sure discriminator is constructed. More generally, it is shown that when R itself depends upon a parameter θ (not necessarily a scalar) and certain broad assumptions are met, one may describe the orthogonal decomposition of P and estimate both a and θ.     

MAXIMUM LIKELIHOOD ESTIMATION OF PARAMETERS OF THE TRUNCATED CAUCHY DISTRIBUTION

Truncated Cauchy distribution with four unknown parameters is considered and derivation and existence of the maximum likelihood estimates is investigated here. We provide a sufficient condition for the maximum likelihood estimate of the scale parameter to be finite, and also show that the condition is necessary for sufficiently large samples. Note that all the moments of the truncated Cauchy distribution exist which makes it much more attractive as a model when compared to the regular Cauchy. We also study, using simulations, the small sample properties of the maximum likelihood estimates.     

Estimating the location of the cauchy distribution by numerical global optimization

The log-likelihood function (LLF) of the single (location) parameter Cauchy distribution can exhibit up to n relative maxima, where n is the sample size. To compute the maximum likelihood estimate of the location parameter, previously published methods have advocated scanning the LLF over a suf-ficiently large portion of the real line to locate the absolute maximum. This note shows that, given an easily derived upper bound on the second derivative of the negative LLF, Brent's univariate numerical global optimization method can be used to locate the absolute maximum among several relative maxima of the LLF without performing an exhaustive search over the real line.     

可能的科斯定理与不可能的科斯主义

“科斯主义”是对“科斯定理”的错误引证。它忽略了被科斯当作分析前提的一个重要事实:利用市场交换制度本身也是一种经济权利。如果“交易权”的界定对市场正常交易具有“新的外部性影响”,那么,“科斯交易”对于社会效率的保证将是不确定的。如果社会成员预见到自己将来无法退出市场制度,那么,在他们之间达成社会契约的前景也是不明朗的。不论“科斯定理”是真理还是谬误,“科斯主义”将社会契约论版本的“科斯定理”用于指导社会构建和经济转轨的做法都隐含着危险。     

Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions

Summary Misclassifications, or noises, in the sampling stage of a Bayesian scheme can seriously affect the values of decision criteria such as the Bayes Risk and the Expected Value of Sample Information. This problem does not seem to be much addressed in the existing literature. In this article, using an approach based on hypergeometric functions and numerical computation, we study the effects of these noises under the two most important loss functions: the quadratic and the absolute value. A numerical example illustrates these effects in a representative case, using both loss functions, and provides additional insights into the general problem. Research partially supported by NSERC grant A 9249 (Canada) and FICU Grant 2000/pas/13. The authors wish to thank colleagues at the University of Alberta in Edmonton, Canada, for very stimulating discussions, and an anonymous referee for drawing their attention to three relevant references that have enriched the content of this final version.     

Banach空间中Hammerstein型积分微分方程初值问题的一种拟上下解法

通过建立一个新的比较原理,利用L-拟上下解方法和混合单调迭代法,研究了Banach空间中一阶非线性积分微分方程初值问题解的存在唯一性,并给出了近似解的迭代序列和误差估计式.     

复调和函数的Cauchy积分公式

建立了复调和函数积分,得出了其Ｃａｕｃｈｙ积分定理与Ｃａｕｃｈｙ积分公式,并讨论了单位圆上复调和函数Ｃａｕｃｈｙ积分公式的特征．     

对称成本企业合作竞争博弈分析

企业间的合作竞争已成为当今世界经济发展战略的大趋势,本文采用Minimax定理来进行合作竞争的战略决策,该决策战略能确保均衡点处达到较高满意度的企业数量较多。将Minimax定理用于线性逆需求对称成本企业合作竞争的产量战略博弈,并与完全竞争市场中的NASH博弈均衡和完全合作均衡进行了对比,最后提出了对付非合作行为的战略。     

Ordinally Bayesian Incentive Compatible Voting Rules

We study strategic voting after weakening the notion of strategy‐proofness to Ordinal Bayesian Incentive Compatibility (OBIC). Under OBIC, truth‐telling is required to maximize the expected utility of every voter, expected utility being computed with respect to the voter's prior beliefs and under the assumption that everybody else is also telling the truth. We show that for a special type of priors, i.e., the uniform priors, there exists a large class of social choice functions that are OBIC. However, for priors that are generic in the set of independent beliefs, a social choice function is OBIC only if it is dictatorial. This result underlines the robustness of the Gibbard–Satterthwaite Theorem.