Variable Selection of Varying Dispersion Student-t Regression Models

The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of means and regression coefficients.In this paper,the varying dispersion Student-t regression model is discussed,in which both the mean and the dispersion depend upon explanatory variables.The problem of interest is simultaneously select significant variables both in mean and dispersion model.A unified procedure which can simultaneously select significant variable is given.With appropriate selection of the tuning parameters,the consistency and the oracle property of the regularized estimators are established.Both the simulation study and two real data examples are used to illustrate the proposed methodologies.     

GMDH-Based Outlier Detection Model in Classi?cation Problems

In many practical classification problems, datasets would have a portion of outliers, which could greatly affect the performance of the constructed models. In order to address this issue, we apply the group method of data handing(GMDH) neural network in outlier detection. This study builds a GMDH-based outlier detection(GOD) model. This model first implements feature selection in the training set L using GMDH neural network. Then a new training set L can be obtained by mapping the selected key feature subset. Next, a linear regression model can be constructed in the set L by ordinary least squares estimation. Further, it eliminates a sample from the set L randomly every time, and then rebuilds a linear regression model. Finally, outlier detection is realized by calculating Cook's distance for each sample. Four different customer classification datasets are used to conduct experiments. Results show that GOD model can effectively eliminate outliers, and compared with the five existing outlier detection models, it generally performs significantly better. This indicates that eliminating outliers can effectively enhance classification accuracy of the trained classification model.     

基于抗差最小二乘配置的海底地形生成研究

最小二乘配置算法能同时顾及测深数据的系统性和随机性影响,提高海底地形的生成精度。根据该算法建立了海洋测深多波束数据的函数模型和随机模型,并构建海底地形。为避免测深数据的异常值影响,进一步推导了基于抗差估计的协方差函数求解公式,提出抗差最小二乘配置算法生成海底地形。利用多波束数据生成海底,结果显示抗差最小二乘配置算法能在构建海底地形的同时准确剔除测深异常。将构建的地形与双线性多项式内插生成的海底进行比较,进一步说明了该算法具有较高的海底地形生成精度。

Abstract：

Seabed terrain generating precision can be improved by least-squares collocation algorithm which takes the systematic and stochastic effects in the bathymetry data. The functional model and stochastic model of the algorithm were created by multibeam bathymetry data,and the method of creating seabed terrain by Least-squares Collocation was researched. To avoid the effect of outliers in bathymetry data,covariance function was calculated by robust estimation,and the Robust Least-squares Collocation algorithm for terrain generation was proposed. It was applied to the real bathymetry data set,and the results indicate that the outliers are detected by the algorithm while the seabed terrain is generated. In the remainder,the terrain grids was compared with which created by bilinear polynomial interpolation algorithm,and it is proved that the Robust Least-squares Collocation algorithm can get higher precision of seabed terrain generation while detecting outliers.     

投资机构的影响:多因素定价模型实证分析

CAPM、APT模型以及Fama-French三因素模型等都从不同角度来解释资产价格的变化过程。本文从证券市场主力（机构投资）着手．分析了多因素定价模型。通过中国证券市场的数据实证检验了多因素定价模型投资机构定价因子的存在。     

Statistical Diagnosis for HIV Dynamics Based on Mean Shift Outlier Model

Ordinary differential equation(ODE) are widely used for quantifying HIV viral dynamics.It is interesting but challenging to estimate ODE parameters from noisy data, especially when the data have some outliers. In this study, the authors use the Mean Shift Outlier Model(MSOM) to detect outliers in HIV model based on the two-step estimation of ODE. Approximate formula for shift parameter is derived. Furthermore, a score test statistic is constructed and its approximating distribution is established. The simulation results show that: 1) The boundary points have more impact on the parameter estimation relative to interior points. 2) The proposed procedure can detect the outliers effectively. The authors illustrate the proposed approach using an application example from an HIV clinical trial and find similar pattern to the simulation studies.     

线性回归模型的非线性稳健估计——基于经验过程理论的研究

线性回归模型参数估计的有效性及对厚尾扰动和离群值的稳健性有进一步改进的余地.本文基于条件分布函数提出线性参数模型的一种新的非线性稳健估计量,利用经验过程理论证明了其相合性和渐近正态性.相对于OLS(ordinary least squares)估计量和常用的稳健LAD(least absolute deviations)和Huber估计量,此估计量可全面把握因变量的分布信息,较准确地由样本数据反映真正的数据生成过程,关于扰动项的厚尾分布具有更好的稳健性,且可更好地消弱极端离群值样本对参数估计的不良影响.多种实验设计的模拟表明,此估计量在有限样本下表现良好;在厚尾扰动或离群值出现的时候,显示出良好的稳健性,且优于OLS、LAD以及Huber估计量的小样本表现.     

异常数据恒虚警检测的非参数方法

针对异常数据和/或数据序列的检测,根据再生核希尔伯特空间最大平均偏差异常数据和/或数据序列检测算法,发展出了一种恒虚警检测异常的非参数方法。将来自正常数据的最大平均偏差描述成了一个统计分布,分析表明:奈曼—皮尔逊假设检验可利用这个分布来进行异常假设检验,而bootstrap重采样技术或期望最大算法则可估计出正常数据或数据序列的统计分布,尽管在给定虚警率的条件下,异常假设检验所需的判决门限可由估计到的统计分布计算获得,但可以利用蒙特卡罗积分的方法来简化这个计算。数值仿真的结果验证了提出方法的有效性,同时,表明所提方法优于文献中报道的方法。     

准最佳加权有序统计恒虚警检测器

为了提高恒虚警检测器在均匀背景中的检测性能及增强对干扰的鲁棒性,本文提出了一种准最佳加权有序统计恒虚警检测器,并应用了文献[3]提出的自动筛选技术。在Swerling Ⅰ型目标及瑞利杂皮假设下,本文推导出了它的P_(fa)、P_d及ADT的数学解析表达式。分析结果表明,它在均匀背景和杂波边缘背景中的性能均比TM获得了改善,同时对多目标也呈现了较好的鲁棒性。在特殊情况下,QBW退化为CMLD。     

Diagnostics in Linear Regresion Model

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截断非平衡似无关模型的极大仿真似然估计

样本数据缺失和截断是现代统计调查中经常遇到的两个问题，它们在一定程度上影响模型参数估计的准确性和有效性. 该研究首先提出了一个新的截断非平衡似无关回归模型，这个模型能够同时考虑数据缺失和截断的特征；然后基于Geweke-Hajivassiliou-Keane（GHK）的仿真算子，建立了该模型的极大仿真似然估计方法；蒙特卡罗实验结果表明，在大样本和有限样本下这种估计方法在参数估计的准确性和有效性方面均具有良好表现.     

GLM约束估计及病态问题研究

利用Ｌａｇｒａｎｇｅ乘子方法解决了广义线性模型（ＧＬＭ）的约束估计问题，并由此引出了广义线性模型的病态问题。通过从减小参数估计的均方误差及消除自变量间的多重共线性着手，本文探讨了改进病态矩阵有效方法。     

基于辅助粒子滤波的风估计方法研究

对飞行中风场测量值含连续野值较多的问题,提出了将连续野值当作噪声处理的方法。噪声设置为随机游走模型并在状态方程中引入时变系数,利用辅助粒子滤波(APF)处理。与当前的自适应Kalman方法进行了比较,在含10个连续野值的模拟数据处理中,Kalman方法发生了跳变,而APF方法成功地处理了连续野值;APF方法和Kalman方法的平均均方误差分别为0.8313和1.0021。最后,将APF方法用于飞行测量数据处理。结果表明,APF方法能处理更多的连续野值,具有更好的精度和稳定性,适合工程应用。     

基于灰色关联分析的软件工作量估算方法

针对历史数据少、信息贫乏的软件估算问题,提出了一种基于灰色关联分析的工作量估算方法。首先结合灰色关联理论分析了项目特征与工作量的关联度,然后利用回归技术选取最优特征集;在此基础上,计算新项目和历史项目的关联度,并根据关联度大的项目估算软件工作量;最后通过4个典型的软件数据集对估算方法的性能进行分析。实验结果表明,该方法能够在历史数据少的情况下准确估算出软件工作量,其性能优于基于回归分析、BP神经网络和类比估算等方法;而选取最优特征后的灰色关联方法,由于剔除了与工作量相关程度低的特征因子,进一步减小了工作量估算的平均误差率。     

非线性递推部分最小二乘及其应用

部分最小二乘回归(PLS)可较好地解决变量间的共线性问题,目前被广泛地应用于过程建模和监控.本文将递推PLS(RPLS)算法同RBF网络相结合,给出了一种非线性递推PLS方法(NRPLS),可根据在线数据自适应地调整模型结构和参数,使模型适应非线性过程的变化.在确定RBF网络的隐层节点参数时,采用了一种改进的k-means聚类算法,自动确定最优的聚类区数.该递推算法用于聚丙稀熔融指数软测量模型的在线修正,取得了较好的效果.     

基于离散PSO的软测量辅助变量选择算法

工业对象的复杂化带来了可测变量的增多,这些变量集合中大量冗余的信息会降低软测量建模的精度。针对这个问题,提出了基于离散PSO的软测量辅助变量选择算法。算法将传统PSO连续的优化过程通过对粒子位置的隶属度计算,将其离散成0或1。0、1分别表示某变量未被选中和被选中,每个粒子就代表一种变量选取情况。将PLS回归用于适应度函数的计算,有利于克服多元回归中多重共线问题。最后,将该算法用在了丙烯精馏塔塔顶丙烯浓度的软测量实验中,实验结果表明该方法有效,并提高了模型的预测精度。     

Robust estimation of parameters in nonlinear ordinary differential equation models

Ordinary differential equation (ODE) models are widely used to model dynamic processes in many scientific fields. Parameter estimation is usually a challenging problem, especially in nonlinear ODE models. The most popular method, nonlinear least square estimation, is shown to be strongly sensitive to outliers. In this paper, robust estimation of parameters using M-estimators is proposed, and their asymptotic properties are obtained under some regular conditions. The authors also provide a method to adjust Huber parameter automatically according to the observations. Moreover, a method is presented to estimate the initial values of parameters and state variables. The efficiency and robustness are well balanced in Huber estimators, which is demonstrated via numerical simulations and chlorides data analysis.     

一类快速模糊支持向量机

由H.P.Huang、C.F.Lin等人和T.Inoue,S.Abe等人提出的两类模糊支持向量机是两种类型的改进支持向量机,分别克服了过学习问题和减少了多类问题分类时存在的不可分区域。如何处理异常数据和加速训练大规模数据集是支持向量机中的急需解决的两个问题。针对这两个问题,提出了一类将两类模糊支持向量机集成的快速模糊支持向量机。训练时,根据每类数据与其类中心的距离,定义隶属函数,以加大对容易被错分样本的惩罚,利用合适的参数λ选取了每类数据中隶属度值较大的边缘数据构造模糊支持向量机,测试时,利用1-a-1和模糊支持向量机的决策函数判定未知样本的类别。含有异常数据的两类问题和机器学习数据集中手写数字识别的多类问题的实验结果,验证了提出的快速模糊支持向量机减少了训练时间同时提高了学习机的推广能力。     

一种抗野值的Kalman滤波器

在目标跟踪系统中,由于杂波的存在,往往使跟踪检测数据中含有大量、成片的野值,造成系统跟踪精度下降。本文通过对检测数据中新息特性的分析,给出了检测数据中野值的判定方法,通过重新构造状态估计来消除野值的影响。仿真结果证明了该方法可有效的剔除野值,提高跟踪系统的跟踪精度。     

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.     

Novel algorithm for constructing support vector machine regression ensemble

1 .INTRODUCTIONRecently , support vector machine (SVM)[1]is anovel and promising technique in the fields of ma-chine learning and classification or regression pre-diction accompanying artificial neural network.InSVM,several learning algorithms can be obtainedgiven different inner-product functions named ker-nel functions ,such as polynomial approach,Bayes-ian classification、radial basic function method、multilayer perceptron network[2]. By now,it hasbeen successfully applied in many ar…