A general result in almost sure central limit theory for random fields

In this note, we investigate, under some mild conditions, the almost sure central limit theorem for random fields with general weight sequences.     

Testing for random effect in the Fuller–Battese model

We consider the Fuller–Battese model where random effects are allowed to be from non-normal universes. The asymptotic distribution of the F-statistic in this model is derived as the number of groups tends to infinity (is large) and sample size from any group is either fixed or large. The result is used to establish an approximate test for the significance of the random effect variance component. Robustness of the established approximate test is given.     

Some remarks on experimental design for estimating the expectation of a stationary random process

For estimation of the mean of a stationary random process the variance-optimal choice of the observation points (the so called experimental design) is considered. For this discrete and continuous designs are introduced, some known results of process statistics are interpreted to experimental design and a proposal for simplification of the minimization problem is offered, moreover it is proved, that for monotone decreasing eovarianee functions a design, for which the points near the ends of the observation interval are more dense than in the middle, is better than the equidistant design.     

Contingency Strategies in Managing Supply Systems with Uncertain Lead‐Times

The globalization of markets and geographic dispersion of production facilities, combined with a heavy outsourcing of supply chain processes, have substantially increased the exposure of supply chains to supply lead‐times of long and uncertain nature. In this paper, we study the potential use of two contingency strategies on top of the conventionally used time buffer—statically planned safety lead‐time (SL)—approach to deal with the lead‐time uncertainty. These are (1) the ex‐ante planning for disruption safety stock (DSS) to be released when a “disruption” (in this case, late delivery of the order) occurs; and (2) the ex‐post dynamic emergency response (DER), which dynamically decides on the timing and size of an emergency order to be placed. Our work elaborates on the optimal parameter setting for these strategies, compares their added values when used to complement the traditional SL approach, and examines how the use of the contingency strategies affects the SL and corresponding cycle length of a periodic review system. Our research finds that: (1) the above contingency strategies reduce the reliance on the SL and are cost effective when the coefficient of variation (CV) of the uncertain lead‐time is high; (2) it is important to re‐optimize the SL to account for the contingency plans; and (3) re‐optimization of the cycle length to account for the presence of the contingency responses, as opposed to using an EOQ‐determined cycle length, does not significantly improve the cost performance. However, such re‐optimization does well in the SL approach when the CV of the uncertain lead‐time is high.     

基于改进可行方向法和随机方向法的V带传动优化

结合可行方向法和随机方向法2种优化方法的优点,提出改进的优化方法用于V带设计,首先利用随机方向法 产生初始点,当随机方向法产生随机方向时则以可行方向法产生可行方向的条件进行约束,对随机单位矢量进行甄选, 只有同时符合可行条件和下降条件的单位矢量方可作为可行搜索方向,在沿选定搜索随机方向进行搜索时利用梯度法 求导确定最佳步长,避免加速步长法的重复迭代。改进后的优化方法结合两者的优点并克服相应的不足,减少产生随机 单位矢量的数量,提高了优化效率。计算实例表明改进的方法可靠、有效。     

多因素扰动情景下应急数量弹性契约的供应链协调

研究突发事件发生导致多种因素干扰的情景下,数量弹性契约是否能实现二级供应链协调,并寻找供应链协调时最优订货与定价策略。针对市场价格稳定和随机两种情况,设定契约弹性系数为常量,分别建立市场价格稳定不变与随机波动两种情况下的应急数量弹性契约模型,寻找它们实现协调的内在约束条件,并与基准模型下的结论进行比较。然后将契约弹性系数由常量拓展为变量,判断是否同时存在最优的弹性系数和订货量,分析弹性系数的变化对于生产、订货决策及供应链整体收益的影响。研究结果证明：当弹性系数为常量时,只要对基准契约的批发价进行适当调整,供应链就能协调应对两种情景下的突发事件,此时,可以找到唯一的最优订货决策。当弹性系数为变量时,两种情景下的供应链均不存在唯一的最优订货决策,但存在唯一的最优供货决策,并且契约弹性系数的改变不会影响供应链期望收益。最后通过算例验证了上述结论的正确性。     

An extension of the placebo‐based pattern‐mixture model

Pattern‐mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data in longitudinal studies. The placebo‐based pattern‐mixture model handles missing data in a transparent and clinically interpretable manner. We extend this model to include a sensitivity parameter that characterizes the gradual departure of the missing data mechanism from being missing at random toward being missing not at random under the standard placebo‐based pattern‐mixture model. We derive the treatment effect implied by the extended model. We propose to utilize the primary analysis based on a mixed‐effects model for repeated measures to draw inference about the treatment effect under the extended placebo‐based pattern‐mixture model. We use simulation studies to confirm the validity of the proposed method. We apply the proposed method to a clinical study of major depressive disorders. Copyright © 2013 John Wiley & Sons, Ltd.     

The Maximum of Independent Geometric Random Variables as the Time for Genomic Evolution

□ We calculate the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, geometric random variables. In many cases, the limit distribution turns out to be the standard Gumbel. The motivation comes from a variant of the genomic evolutionary model proposed by Wilf and Ewens^{[ 15} Wilf , H.S. , Ewens , W.J . There's plenty of time for evolution . Proc. Nat. Acad. Sci. 2010 , 107 ( 52 ), 22454 – 22456 , doi: 10.1073/pnas.1016207107. [Crossref], [PubMed] , [Google Scholar] ^] as an answer to the criticism of the Darwinian theory of evolution stating that the time required for the appropriate mutations is huge.

A byproduct of our analysis is the asymptotics of the moments as well as the limiting distribution (after the appropriate normalization) of the maximum of independent, not identically distributed, exponential random variables.