A new sequential design based on the robbins-monro procedure

Summary A sequential estimation procedure based on the Robbins-Monro process is proposed. Through observations of a random variableY(x), estimates of a regression functionM(x) are obtained, whereM(x)=E[Y(x)]. The estimates of the roots ofM(x) are shown to be strongly convergent and asymptotically normal with minimum variance.     

KMT-type inequalities and goodness-of-fit tests

The implications of the probability inequality of Komløs, Major and Tusnády (1975) for the theory of goodness-of-fit tests, especially tests based on stochastic integrals with respect to the basic martingale in the random censoring model, are discussed. Choices of the integrand of the stochastic integral which yield highly efficient generalized rank and supremum type tests are given for the simple as well as the composite null hypothesis.     

Optimal order placement in limit order markets

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by characteristics of the order flows and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows the study of how the optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algorithm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.     

Orlicz空间中的联合最佳逼近(续)

我们在文献[1]中研究了在 Orlicz 空间 L+M~*中关于 Luxemburg 范数‖·‖_(M)的联合最佳逼近问题,本文在 Orlicz 空间 L_M~*中关于 Orlicz 范数‖·‖_M 研究类似的问题,本文中的结果是文献[1]中结果的继续。     

推广的多变量Bernstein—Kantorovi 多项式在Lp—空间的逼近

关于二元函数 f(x,y)的 Kantorovi 多项式的逼近问题谢敦礼在文中进行了研究,并得到某些结果,本文在引进推广 Bernstein—Kantorovi 多项式概念的基础上,得到两个新定理,它推广和改进了文中的结果。     

周期信号调制色泵噪音驱动下单模激光的稳态平均光强相对涨落

研究了周期信号调制噪音驱动下单模激光系统的统计性质,采用线性化近似方法,计算了系统的稳态平均光强相对涨落C(0),分析了色泵噪音强度P、量子噪音强度Q、色泵噪音自关联时间τ、输入信号振幅B和频率Ω等对稳态平均光强相对涨落的影响。结果表明,C(0)随P、Q和B单调上升,随Ω单调下降。在色泵噪音自关联时间长、小噪音、信号振幅不大和频率较高的条件下稳态平均光强相对涨落较小。     

商业银行风险管理中的模糊分析方法

将商业银行面临的风险分解成若干个风险因素子系统,以金融理论为指导建立各子系统风险因素评价的隶属度矩阵,并在此基础上采用模糊间接识别模型及贴近度的概念,构造各子系统风险因素模糊识别模型;通过各子系统模糊识别模型的合成,建立整个商业银行系统的模糊识别模型,借以达到各商业银行风险排序、化解金融隐患之目的。     

Plug‐in bandwidth selector for recursive kernel regression estimators defined by stochastic approximation method

In this paper, we propose an automatic selection of the bandwidth of the recursive kernel estimators of a regression function defined by the stochastic approximation algorithm. We showed that, using the selected bandwidth and the stepsize which minimize the mean weighted integrated squared error, the recursive estimator will be better than the non‐recursive one for small sample setting in terms of estimation error and computational costs. We corroborated these theoretical results through simulation study and a real dataset.     

Economic lot and delivery scheduling problem for multi-stage supply chains

The economic lot and delivery scheduling problem for a multi-stage supply chain comprising multiple items is studied in this paper. It is required to develop a synchronized replenishment strategy, and specify the sequence of production and the replenishment cycle time that achieves synchronization through the supply chain at minimum cost. The problem is presented in a novel formulation based on the quadratic assignment representation. The common cycle time and the integer multipliers policies are adopted to accomplish the desired synchronization. The two policies are represented by nonlinear models handled through a hybrid algorithm. The algorithm combines linearization, outer approximation and Benders decomposition techniques. Results of the two policies demonstrate that a cost reduction up to16.3% can be attained by employing the integer multipliers policy instead of the common cycle time. Computational experiments show the efficiency of the new formulation and solution algorithm by reaching the optimal solution for large problem instances in short time.