Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

体词谓语句的生成条件

体词谓语句是以体词作谓语,能够自由生存的句子,它是现代汉语中一种独立的句型而非动词句的省略。体词具备陈述功能,是其作谓语的语法条件,体谓句的陈述关系,主要是由两个单独体词间的并列、偏正关系,因修饰语的参与转化而来的。从语义角度说,体谓句中主谓两部分的逻辑关系、语义制约,以类的形式出现,是句子赖以存在的基础。     

Estimation of critical points in the mixture inverse Gaussian model

The maximum likelihood estimation for the critical points of the failure rate and the mean residual life function are presented in the case of mixture inverse Gaussian model. Several important data sets are analyzed from this point of view. For each of the data sets, Bootstrapping is used to construct confidence intervals of the critical points.     

Comparative probability for conditional events: A new look through coherence

We study, from the standpoint of coherence, comparative probabilities on an arbitrary familyE of conditional events. Given a binary relation ·, coherence conditions on · are related to de Finetti's coherent betting system: we consider their connections to the usual properties of comparative probability and to the possibility of numerical representations of ·. In this context, the numerical reference frame is that of de Finetti's coherent subjective conditional probability, which is not introduced (as in Kolmogoroff's approach) through a ratio between probability measures.Another relevant feature of our approach is that the family & need not have any particular algebraic structure, so that the ordering can be initially given for a few conditional events of interest and then possibly extended by a step-by-step procedure, preserving coherence.     

Three pseudo-paradoxes in ‘quantum’ decision theory: Apparent effects of observation on probability and utility

In quantum domains, the measurement (or observation) of one of a pair of complementary variables introduces an unavoidable uncertainty in the value of that variable's complement. Such uncertainties are negligible in Newtonian worlds, where observations can be made without appreciably disturbing the observed system. Hence, one would not expect that an observation of a non-quantum probabilistic outcome could affect a probability distribution over subsequently possible states, in a way that would conflict with classical probability calculations. This paper examines three problems in which observations appear to affect the probabilities and expected utilities of subsequent outcomes, in ways which may appear paradoxical. Deeper analysis of these problems reveals that the anomalies arise, not from paradox, but rather from faulty inferences drawn from the observations themselves. Thus the notion of quantum decision theory is disparaged.     

同类异质产品市场博弈Nash均衡最优策略模型

本文按照Nash均衡解的要求,建立同类异质产品市场用户需求分布及效用结构模型,导出不同定位的企业所实施竞争策略的若干最优条件,通过计算不同策略设计下产品相应的临界功能效用值,参与竞争的企业可找到适合于市场需求的最优决策。     

中国股市收益率分布函数研究

本文在考察了文献中描述股票收益率的各类分布函数的基础上,以稳定Paretian分布与t分布为备择,研究了沪、深股市各类综指收益率的分布函数的形式,并对分布函数的参数进行了估计。     

基于模糊规划的QFD 系统参数确定方法

针对QFD 系统的内在模糊性,运用带有对称三角形模糊系数的模糊规划理论,提出了一 种确定QFD 系统参数的方法. 并通过工程特性目标值的规范化,定义产品开发总成本函数、工 程特性改进成本函数及改进成本系数等概念,建立了一个QFD 规划模型. 仿真结果表明,该模 型能够帮助开发人员在不确定的、模糊条件下有效确定关联函数及自相关函数,优化顾客需求 的满意水平,确定工程特性目标值,使新开发/ 改进的产品顾客满意度赶上或超过目标市场上 的竞争企业,并满足开发预算约束.     

On the Effect of Probability Distributions of Input Variables in Public Health Risk Assessment

A central part of probabilistic public health risk assessment is the selection of probability distributions for the uncertain input variables. In this paper, we apply the first-order reliability method (FORM)^(1–3) as a probabilistic tool to assess the effect of probability distributions of the input random variables on the probability that risk exceeds a threshold level (termed the probability of failure) and on the relevant probabilistic sensitivities. The analysis was applied to a case study given by Thompson et al. ⁽⁴⁾ on cancer risk caused by the ingestion of benzene contaminated soil. Normal, lognormal, and uniform distributions were used in the analysis. The results show that the selection of a probability distribution function for the uncertain variables in this case study had a moderate impact on the probability that values would fall above a given threshold risk when the threshold risk is at the 50th percentile of the original distribution given by Thompson et al. ⁽⁴⁾ The impact was much greater when the threshold risk level was at the 95th percentile. The impact on uncertainty sensitivity, however, showed a reversed trend, where the impact was more appreciable for the 50th percentile of the original distribution of risk given by Thompson et al. ⁴ than for the 95th percentile. Nevertheless, the choice of distribution shape did not alter the order of probabilistic sensitivity of the basic uncertain variables.