Prediction with a Generalized Cost of Error Function

Classical prediction theory limits itself to quadratic cost functions, and hence least-square predictors. However, the cost functions that arise in practice in economics and management situations are not likely to be quadratic in form, and frequently will be non-symmetric. It is the object of this paper to throw light on prediction in such situations and to suggest some practical implications. It is suggested that a useful, although sub-optimal, manner of taking into account generalized cost functions is to add a constant bias term to the predictor. Two theorems are proved showing that under fairly general conditions the bias term can be taken to be zero when one uses a symmetric cost function. If the cost function is a non-symmetric linear function, an expression for the bias can be simply obtained.     

基于非对称损失函数的过程均值与标准差优化设计

质量特性的过程均值与过程标准差的选定是一个重要的命题,它们是影响质量成本的重要因素.由顾客定义的特性目标均值以及初始标准差往往并不一定能使得总体的质量损失最小化。针对此问题,本文首先讨论了非对称的质量损失函数,并在此基础上构造出质量特性目标均值与标准差的优选模型,进而得到最优目标过程均值与标准差。在模型的应用中表明:其他情况不变的情况下,质量特性最优均值与最优标准差对质量损失系数具有一定的稳健性。     

具有重尾或异方差误差的双变量预测回归模型的中位无偏估计

In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heterescedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.     

Median Unbiased Estimation of Bivariate Predictive Regression Models with Heavy-tailed or Heteroscedastic Errors

In this paper, we consider median unbiased estimation of bivariate predictive regression models with non-normal, heavy-tailed or heteroscedastic errors. We construct confidence intervals and median unbiased estimator for the parameter of interest. We show that the proposed estimator has better predictive potential than the usual least squares estimator via simulation. An empirical application to finance is given. And a possible extension of the estimation procedure to cointegration models is also described.     

Asymmetric Supply Function Equilibria with Forward Contracts

We consider markets in which firms offer supply functions, rather than a quantity or price alone: the most important examples are wholesale electricity markets. The equilibria in such markets can be hard to characterize. In many cases, whole families of supply function equilibria occur so there are difficulties in determining which equilibrium will be chosen. In this paper, we consider supply function equilibria, when firms hold forward contracts, which is common in electricity markets. Under the assumption that contract positions have been fixed in advance, we characterize the families of supply function equilibria in a duopoly. The existence of forward contracts implies a tightening of the conditions for an equilibrium, and a greater likelihood that no equilibrium solution exists. In the case of three firms, there can be at most one supply function equilibrium, provided that the lowest demand be small enough.     

基于错误系统理论的和式型和向量型错误函数研究

研究了和式型和向量型函数的相关定义及性质,为更好的描述错误系统,以及计算错误值奠定了基础.     

广义Taylor中值函数若干分析性质

文[2-8]对微分中值定理及Taylor定理"中间点"的渐近性质进行了研究,本文在此基础上,给出了"广义Taylor中值函数"的定义,对"广义Taylor中值函数"的分析性质进行了系统的讨论,证明了"广义Taylor中值函数"的单调性、可积性、连续性、可微性等分析性质.     

非对称绝对线性损失下正态总体的参数设计

田口玄一提出了很多损失函数,其中二次损失是应用最为广泛的一种。当实际损失函数不是二次损失函数而使用二次损失时,就会引起参数设计的不正确。在某些情况下,线性损失函数更适合工业应用。本文在非对称的线性损失下,讨论了参数设计的可行性,证明田口先生方法的稳健性设计和灵敏度设计依然行之有效。结果表明性能指标平均值必须稍微偏离目标值,才能使平均损失达到最小。     

Submodular Flow Problem with a Nonseparable Cost Function

Received: February 19, 1996     

基于非对称损失函数的参数设计

本文针对望目特性的正态指标,在非对称的二次质量损失函数下,讨论了参数设计的可行性, 证明田口方法的稳健性设计和灵敏度设计依然行之有效.定义了调整参数,求出了使质量损失最小的数值解,并给出了参数设计的具体步骤.     

Infinite Time-Dependent Network Equilibria with a Multivalued Cost Function

In this paper, we consider the dynamic traffic network equilibria with possibly an infinite number of routes, a possibly multivalued cost function, and a not necessarily reflexive Banach space of flow trajectories. We investigate the existence of equilibria under a monotonicity assumption on the cost function, as well as an equivalent condition for equilibria under additional constraints. Finally, we give an iterative method for the computation of equilibria. Our results generalize and extend previous results in Refs. 1–2.Communicated by F. GiannessiThe authors are thankful to the referee and Professor F. Giannessi for valuable suggestions and comments leading the paper to its present form.All correspondence should be sent to the first author.     

线性不对称损失时非正态分布过程均值优化

针对常见的两种非正态分布———梯形分布和三角分布,研究线性不对称质量损失时其过程均值的优化问题,建立了梯形分布在五种不同情况下线性不对称质量损失的数学模型,基于以上模型给出了线性不对称质量损失时梯形分布最优过程均值的确定方法;研究三角分布在四种不同情况下线性不对称质量损失的数学模型,并给出了线性不对称质量损失时三角分布最优过程均值的确定方法。最后,用实例验证本过程均值优化模型的有效性。实例表明,应用线性不对称损失函数,适当的改变过程均值,可以有效地降低产品的质量损失,通过调整工艺过程将获得最佳经济效益。     

一个非对称线性风险函数与证券组合投资分析

在分析Jia&D yer的风险-价值理论基础上,给出了一个基于预先给定的目标收益的非对称线性风险函数.该风险函数是低于参考点的离差和高于参考点的离差的加权和,它利用一阶"上偏矩"来修正一阶下偏矩,进一步建立了在此非对称风险函数下的线性规划证券投资组合模型;并证明了该模型与二阶随机占优准则的一致性;最后通过上海证券市场的实际数据验证了该模型的有效性和实用性.     

On an Error Term Related to the r-th Power of the Euler Totient Function

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A Predictive Model for the Police Response Function

The expected response time to a call for service (CFS) for a given configuration of police beats is developed. The effect of downtime calls on the response time to a CFS is determined. Consideration is given to both travel time and waiting time. Travel time and service time distributions are isolated. The model is valid for Poisson arrivals and arbitrary service time distributions. A probabilistic assignment policy is determined for each beat. The fraction of incoming calls arriving in beat k answered by unit l is obtained. Pre-emptive priorities are allowed. Application to the Aurora, Illinois, Police Department is shown.     

The Median Stabilization Degree of a Median Algebra

The median stabilization degree (msd, for short) of a median algebra measures the largest possible number of steps needed to generate a subalgebra with an arbitrary set of generators. We determine the value of msd of a graphic n-cube Qn and we derive an estimation of msd for the natural median operator of Rn which is sharp up to one or two units. Interestingly, msd of Qn and of Rn grows like log1.5n. Finally, we characterize median algebras and median graphs of msd 1 in terms of forbidden subspaces.     

Continuity of a Metric Function and Projection in Asymmetric Spaces

Mathematical Notes - The article studies the continuity of left metric functions and the upper semicontinuity of left metric projections onto boundedly sequential left-compact sets in asymmetric...     

Refined Error Estimates for Radial Basis Function Interpolation

We discuss new and refined error estimates for radial-function scattered-data interpolants and their derivatives. These estimates hold on R ^d , the d-torus, and the 2-sphere. We employ a new technique, involving norming sets, that enables us to obtain error estimates, which in many cases give bounds orders of magnitude smaller than those previously known.     

灰色Verhulst模型的样条插值函数的残差修正

本用样条函数对灰色Verhulst模型的残差序列进行插值拟合，然后作用于二阶线性微分方程，并以此修正原模型，得到一种新的预测模型的数值解，提高了拟合的精确度。