线性回归模型系数Stein估计的改进研究

针对线性回归模型病态的根本原因,提出了一类新的估计———c-k型估计,将岭估计与Stein估计统一到一个估计类;研究了这一估计类,证明利用岭回归技术可以改进著名的Stein估计(在均方误差意义下);同时研究了相应参数的最优值,分别给出了它的一个上界及下界,为病态线性回归模型系数的有偏估计提供了改进的技术途径.     

Approximating nondominated sets in continuous multiobjective optimization problems

Many important problems in Operations Research and Statistics require the computation of nondominated (or Pareto or efficient) sets. This task may be currently undertaken efficiently for discrete sets of alternatives or for continuous sets under special and fairly tight structural conditions. Under more general continuous settings, parametric characterisations of the nondominated set, for example through convex combinations of the objective functions or ε‐constrained problems, or discretizations‐based approaches, pose several problems. In this paper, the lack of a general approach to approximate the nondominated set in continuous multiobjective problems is addressed. Our simulation‐based procedure only requires to sample from the set of alternatives and check whether an alternative dominates another. Stopping rules, efficient sampling schemes, and procedures to check for dominance are proposed. A continuous approximation to the nondominated set is obtained by fitting a surface through the points of a discrete approximation, using a local (robust) regression method. Other actions like clustering and projecting points onto the frontier are required in nonconvex feasible regions and nonconnected Pareto sets. In a sense, our method may be seen as an evolutionary algorithm with a variable population size. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

一种发动机万有特性曲面拟合的新方法

通过分析发动机实测试验数据,提出了燃油消耗率同转速和扭矩之间存在类似幂指函数的关系,运用多元回归的方法对发动机的万有特性曲面进行了拟合,对拟合结果用数理统计的方法进行了检验,最后指出对发动机万有特性曲面的拟合采用分段函数进行数值计算,将得到更为精确的结果。     

回归型支持向量机的机翼结冰冰型预测

飞机结冰严重威胁着飞行安全。针对机翼结冰冰型预测时不确定性因素较多、难以准确预测的问题,提出了一种基于回归型支持向量机的机翼结冰冰型预测方法。在建立冰型模型的基础上,利用回归型支持向量机(Support Vector Regression,SVR)获得冰型多项式系数,从而预测出相关飞行条件和大气条件下的冰型。仿真结果表明,该方法具有较好的预测能力,可以及时提供可靠的结冰信息,为保证结冰条件下的飞行安全提供了保障。     

A mathematical programming approach for improving the robustness of least sum of absolute deviations regression

This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least‐sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

高层建筑物变形监测与分析方法研究

进行高层建筑物的变形监测对其安全性非常重要。本文针对高层建筑物变形监测环境及其对监测快速、高精度的要求,详细阐述了采用GPS和全站仪的组合监测方案,重点提出了利用回归平面进行建筑物整体倾斜变形分析的方法,并用实例验证了该方法的可行性。     

基于误差传递和逐步回归法的火控系统精度分析

利用坐标变换得到射击诸元解算模型,根据得到的射击诸元解算模型的教学表达式,用隐函数微分法得到每个射击诸元影响因素的误差传递系数,利用精度分析模型建立射击诸元精度表达式.然后用均匀试验设计法确定典型射击条件,在这些典型射击条件下,计算各误差传递系数,根据给定的某组火控系统各设备的精度指标,进而计算火控系统各典型射击条件下的火控系统精度值,并确定合理的精度指标期望值.要获得这组火控系统各设备的精度指标下,任意指定射击条件下的系统精度值,利用已算出的各典型射击条件下的系统精度值,采用逐步回归分析方法,可获得火控系统各射击诸元参数的精度与各射击条件的函数关系近似表达式.     

基于采样的非线性滤波方法

在系统阐述贝叶斯估计理论的基础上,分析和总结了扩展卡尔曼滤波、Sigma点卡尔曼滤波以及粒子滤波等方法的特点、使用条件以及局限性.介绍了扩展卡尔曼滤波方法并指出其缺陷;介绍了无轨迹卡尔曼滤波、中心差分卡尔曼滤波等确定性采样方法,并在加权统计线性回归意义下将其归结为Sigma点卡尔曼滤波方法;介绍了随机采样方法-粒子滤波方法,并指出其主要的研究方向.最后,对非线性滤波的发展趋势进行了展望.     

军用飞机采购价格预测研究

分析了我国军用飞机价格预测中存在的困难,从我国国情出发,提出了我国军用飞机价格预测的两种方法:根据制造成本和期间费用预测价格方法与相似飞机预测价格方法.相似飞机预测法是指采用偏最小二乘回归、神经网络或灰色理论等方法,根据相似飞机的性能与价格数据建立价格预测模型,实例表明,相似飞机价格预测法具有较高的精度.     

矿产统计预报的多元信息复合方法及预测模型

如何有效地利用多种信息进行矿产统计预报是一个有经济效益的课题。本文运用多信息复合思想,采用回归分析、判别分析和集成预报等方法使矿物预报的正确概率大大提高。