Bf—稳健的Mallows型回归估计量

讨论了Ｍａｌｌｏｗｓ型回归估计的拟合值影响，构造一类Ｂｆ－稳健的Ｍａｌｌｏｗｓ型回归估计量，并证明了它的存在性和可容许性。     

非参数回归函数的稳健Bootstrap

在有异常值的数据中,Bootstrap样本可能比原有样本含有更高的“污染”,这会降低所要做的统计推断的有效性.本文讨论在非参数回归N-W估计中,如何利用影响函数得到重新抽样的概率,使用倾斜的Bootstrap方法得到曲线的拟合,从而达到有效地抵制异常值对回归函数影响的目的,数值模拟的结果表明这种处理方式的有效性.     

基于统计深度函数的G-Q检验

G-Q检验是一种简单、有效的异方差检验方法,但该方法只适用于一个自变量,在多变量情况下,文献[1]利用主成分对样本数据进行排序,得到了G-Q检验的推广.众所周知,主成分分析是一种有效的降维方法,但其在降维的同时伴随着信息的损失,统计深度函数可作为多元数据排序的有效工具.本文基于统计深度函数得到了推广了的G-Q检验,并应用于实例。     

Isotonic Regression under Lipschitz Constraint

The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a better approximation to that function. In this paper, we consider the formulation which assumes that the data were generated by a continuous monotonic function obeying the Lipschitz condition. We propose a new algorithm, the Lipschitz pool adjacent violators (LPAV) algorithm, which approximates that function; we prove the convergence of the algorithm and examine its complexity. The authors were supported by the Intramural Research Program of NIH, National Library of Medicine.     

基于稳健回归的电网高峰负荷预测模型应用

在分析高峰负荷特点的基础上,建立了基于稳健回归模型的高峰负荷预测方法。该方法具有较强的稳健性,适应异常情况下的样本数据,能保持较满意预测精度。通过对辽宁省2002年电网负荷数据的预测模拟,验证了本文高峰预测方法的有效性。     

Poisson-Lindley回归模型基于EM算法的诊断分析(英文)

利用EM算法研究了来自于Lindley分布权重的混合Poisson模型,即Poisson-Lindley回归模型,从而利用基于完全数据似然函数的条件期望进行统计诊断和局部影响分析,得到了几个有用的诊断统计量,并用一个数值实例说明了所得统计量的有效性.     

纵向数据半参数Beta回归模型的影响分析

本将随机效应当作是缺失数据,基于Q函数和EM算法并利用P-样条拟合非参数部分,得到了纵向数据半参数Beta回归模型估计方法.基于数据删除模型,我们得到了模型参数部分的广义Cook距离以及非参数部分的广义DFIT.此外,本文还研究了在四种不同扰动情形下模型的局部影响分析,得到了相应的影响矩阵.最后,我们通过两个数值实例验证了所得诊断统计量的有效性.     

一类基于秩次的稳健线性回归估计与诊断方法

线性回归模型的误差项不服从正态分布或存在多个离群点时,可以将残差秩次的某些函数作为权重引入估计模型来减少离群点的不良影响。本文从参数估计、稳健性质、回归诊断等方面对基于残差秩次的一类稳健回归方法进行介绍.通过模拟研究和实例分析表明,R和GR估计是一种估计效率较高的稳健回归方法,其中GR估计可同时避免X与Y空间离群点,而高失效点HBR估计可通过控制某个参数在稳健性与估计效率之间进行折衷.     

Robust Depth-Weighted Wavelet for Nonparametric Regression Models

In the nonparametric regression models, the original regression estimators including kernel estimator, Fourier series estimator and wavelet estimator are always constructed by the weighted sum of data, and the weights depend only on the distance between the design points and estimation points. As a result these estimators are not robust to the perturbations in data. In order to avoid this problem, a new nonparametric regression model, called the depth-weighted regression model, is introduced and then the depth-weighted wavelet estimation is defined. The new estimation is robust to the perturbations in data, which attains very high breakdown value close to 1/2. On the other hand, some asymptotic behaviours such as asymptotic normality are obtained. Some simulations illustrate that the proposed wavelet estimator is more robust than the original wavelet estimator and, as a price to pay for the robustness, the new method is slightly less efficient than the original method.     

增量式Huber-支持向量回归机算法研究

传统的面向支持向量回归的一次性建模算法中样本增加时,均需从头开始学习,而增量式算法可以充分利用上一阶段的学习成果。SVR的增量算法通常基于ε-不敏感损失函数,该损失函数对大的异常值比较敏感,而Huber损失函数对异常值敏感度低。所以在有噪声的情况下,Huber损失函数是比ε-不敏感损失函数更好的选择,在现实情况当中。基于此,本文提出了一种基于Huber损失函数的增量式Huber-SVR算法,该算法能够持续地将新样本信息集成到已经构建好的模型中,而不是重新建模。与增量式ε-SVR算法和增量式RBF算法相比,在对真实数据进行预测建模时,增量式Huber-SVR算法具有更高的预测精度。     

Bounded influence regression using high breakdown scatter matrices

In this paper we estimate the parameters of a regression model using S-estimators of multivariate location and scatter. The approach is proven to be Fisher-consistent, and the influence functions are derived. The corresponding asymptotic variances are obtained and it is shown how they can be estimated in practice. A comparison with other recently proposed robust regression estimators is made.     

Logistic回归模型的影响分析

Logistic回归模型的影响分析是Logistic回归诊断研究中的重要内容。常用的分析方法都是轮换地删除数据点后的逐步判断,而这个判断的过程主要体现在模型的诊断图上。鉴于此,通过构造诊断统计量来有效地开发诊断图成为影响分析的核心内容,并由此能较为准确地探寻出模型的强影响点。本文通过对Logistic回归模型帽子矩阵的分解以及对轮换地删除数据点后的系数估计的相对变化量进行加权,得出Logistic回归模型诊断图使其能比传统的诊断图更准确地判断出模型的强影响点。     

求解线性模型稳健参数估计的整数编码遗传算法

线性模型回归系数的一些稳健估计如LMS、LQS、LTS、LTA的应用越来越广泛,然而它们的精确计算依赖于NP难题,在遇到高维大规模数据集时不可能在较短时间内得到精确解.为尽快得到较高精度的近似解,提出了求解线性模型的稳健参数估计的整数编码遗传算法,通过计算机模拟试验验证了算法可以更快地找出全局最优解.     

A Frisch-Newton Algorithm for Sparse Quantile Regression

Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Prisch-Newton algorithm for quantile regression described in Portnoy and Koenker~([28]). The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.     

基于多元线性回归分析的民用运输机场旅客吞吐量预测

修建第二机场的必要性以及何时开始修建,取决于该地区的机场旅客吞吐量何时达到饱和.从机场旅客吞吐量的可能影响因素出发,分析各影响因素与旅客吞吐量之间的相关性,并以西南地区某枢纽运输机场为例,建立机场旅客吞吐量的多元线性回归预测模型,预测该机场未来年的旅客吞吐量,并利用时间序列法对所得的预测值进行验证.结果表明,该模型能够较准确的预测出机场未来年的旅客吞吐量,为机场扩建或新建第二机场的必要性提供科学依据.     

The Fast RODEO for Local Polynomial Regression

An open challenge in nonparametric regression is finding fast, computationally efficient approaches to estimating local bandwidths for large datasets, in particular in two or more dimensions. In the work presented here, we introduce a novel local bandwidth estimation procedure for local polynomial regression, which combines the greedy search of the regularization of the derivative expectation operator (RODEO) algorithm with linear binning. The result is a fast, computationally efficient algorithm, which we refer to as the fast RODEO. We motivate the development of our algorithm by using a novel scale-space approach to derive the RODEO. We conclude with a toy example and a real-world example using data from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite validation study, where we show the fast RODEO’s improvement in accuracy and computational speed over two other standard approaches.     

基于岭回归模型大数据最优子抽样算法研究

随着大数据时代的来临,为了提高计算效率,Wang等(2018)提出基于logistic回归的最优子抽样算法,在保证参数估计精度的前提下,节省了大量的运算时间.为解决变量间的多重共线性,文章提出基于岭回归模型的最优子抽样算法,并证明岭回归模型中参数估计的一致性与渐近正态性.利用数值模拟与实证分析对最优子抽样算法进行评估,...     

对稳健回归尺度参数估计的一种改进

常对线性回归模型的稳健 M估计中 ,尺度参数使用绝对离差中位数 MAD.将 Rousseeuw等人对单变量尺度参数的一种稳健估计 Sn引入到回归问题中 ,讨论了此估计的一些优良性质 ,并通过一个小规模的模拟研究 ,说明使用 Sn比使用 MAD做尺度参数将会较大地提高回归估计的估计效率 .     

一类非参数回归函数估计的性质

设Z_(11),z_(12),…,Z_是在固定点(x_i,y_1),1≤≤n_1,1≤j≤n_2,的n_1n_2个观察值,适合模型 Z_(ij)=g(x_i,y_j)+ε_(ij),1≤i≤n_1,1≤j≤n_2。(1) 本文给出了g的一种估计并讨论了估计的性质。     

A COMPARISON BETWEEN TWO ROBUST REGRESSION ESTIMATORS BY MEANS OF ROBUST COVARIANCES

Two classes of Mallows GM-estimators with invariance are considered in the stochastic linear regression model. Some of their asymptotic properties are described, and the fittedvalue influence and variance components are compared by means of robust covariances,