随机删失数据非线性回归模型的最小一乘估计

研究了随机删失数据非线性回归模型的最小一乘(LAD)估计问题, 证明了LAD估计量的渐近性质, 包括相合性、依概率有界性和渐近正态性等. 模拟结果显示对删失数据回归问题, LAD估计仍比最小二乘估计(LSE)稳健.     

VALUE-AT-RISK的核估计理论

如何根据历史数据估计Value-at-Risk（VaR）;是风险分析与管理中一个重要的基本问题.木文基于非参数核估计方法,通过拟合实际数据过程的分布,构造了VaR的估计.在合适的相依数据条件下,证明了该估计量的渐近正态性,并给出了渐近方差的估计.由此表明:本文所构造的估计量不仅比参数模型具有更广泛的适应性,而且如同参数模型具有n~（-1/2）的收敛速度.本文假设的数据过程避免使用混合性,可很好地适用于金融管理中广泛应用的ARMA与GARCH模型族及非线性模型.     

系数函数光滑度互不相同的变系数模型的一步估计法

该文提出了一种一步估计方法用以估计变系数模型中具有互不相同光滑度的未知函数, 所有未知函数和它们的导数的估计量由 一次极小化得到. 给出了估计量的渐近性质, 包括渐近偏差、方差和渐近分布, 一步估计量被证明达到了最优收敛速度.     

误差为FCA过程的线性模型HD估计的渐近正态性

考虑线性回归模型y=x^Tβ+e₁其中误差e是函数系数自回归（FCA）过程.本文研究该模型未知参数的Huber-Dutter估计的渐近性质,在合理的条件下,证明了这些估计量以n^-（1/2）速度渐近于正态分布.     

变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

变系数模型中的逐元B-Spline估计法

给出了一种用于估计变系数模型中未知函数的逐元B-Spline方法,建立了估计量的局部渐近偏差,方差和渐近正态分布,开发了一种快速选择估计量窗宽的方法,通过Monte Carlo模拟研究了估计量的有限样本性质.     

可加模型的两阶段局部M-估计

研究了可加模型分量回归函数的局部M-估计, 针对分量回归函数及其导数提出了两阶段局部M-估计的方法. 在较广泛的条件下建立了估计量的渐近正态性理论, 估计量具有先知性质(oracle property), 即在估计某一分量回归函数时,其他分量回归函数是否已知不影响估计量的渐近性质. 渐近理论包括了两类常用的估计量,即最小二乘估计和最小一乘估计. 当ψ是连续的且是非线性时,估计量的实施非常耗时,为了减轻计算的负担, 提出了一步局部M-估计量, 并证明了在初始估计量足够好的情形下, 一步局部M-估计量与完全迭代所得到的估计量具有相同的渐近估计效率, 这使得两阶段局部M-估计的方法较为实用. 两阶段局部M-估计量继承了局部多项式估计的优点, 同时克服了其在最小二乘准则下不稳健的缺点. 另外, 还讨论了估计方法实施方面的细节及有关参数的选择方法. 数值模拟结果及实际例子说明了两阶段局部M-估计方法的优点及实用性.     

双重时序AR—MA模型的高价平稳性

本文讨论双重时序AR－MA模型的高价（4阶，8阶及一般2m阶）平稳解存在的充分条件，这些结论对建立模型参数的矩估计及讨论估计量的渐近性质都是必不可少的．     

基于分层抽样的校准方法分别比率-乘积估计研究

比率估计在抽样估计阶段利用辅助信息,提高了估计量的估计精度,是抽样调查中一类较为常用的估计方法,但现有的一些比率估计方法均具有各自的最优条件,这在一定程度上影响了它们在实际调查中的应用。为了解决比率估计的最优限制问题,本文引入了校准估计方法,并基于分层抽样研究了总体均值的校准方法分别比率-乘积估计量。在大样本情况下,本文推导了新估计量的估计偏差和均方误差,说明新估计量具有渐近无偏性,并在估计量均方误差最小时,得到了总体参数的渐近最优估计量和渐近最优估计量的方差。在模拟研究中,根据比率估计量的最优条件是否满足,本文生成了两种不同的总体,对比分析了新估计量和现有比率估计量的估计效果,结果表明在两种不同的情况下,新估计量的估计效果均优于现有估计量的估计效果。最后,本文利用一个实际例子,验证了新估计量的有效性和实用性。     

空间半参数变系数部分线性回归中的分位数估计

本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质.     

Least Absolute Deviation Estimation for Regression with ARMA Errors

The asymptotic normality for least absolute deviation estimates of the parameters in a linear regression model with autoregressive moving average errors is established under very general conditions. The method of proof is based on a functional limit theorem for the LAD objective function.     

Weighted least absolute deviations estimation for periodic ARMA models

This paper investigates the weighted least absolute deviations estimator (WLADE) for causal and invertible periodic autoregressive moving average (PARMA) models. Asymptotic normality of the estimator is derived under a fractional moment condition. A simulation study is given to assess the performance of the proposed WLADE.     

LAD estimation for nonlinear regression models with randomly censored data

The least absolute deviations (LAD) estimation for nonlinear regression models with randomly censored data is studied and the asymptotic properties of LAD estimators such as consistency, boundedness in probability and asymptotic normality are established. Simulation results show that for the problems with censored data, LAD estimation performs much more robustly than the least squares estimation.     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

DETERMINATION OF PERMANENT OPTIMAL DATA POINTS AND AN EFFICIENT ALGORITHM FOR LAD PROBLEM

This paper gives a definition of permanent optimal data point of Least Absolute Deviation(LAD)problem.Some theoretical results on non-degenerate LAD problem are obtained.For computing LAD problem,an efficient,algorithm is given according to the idea of permanent optimal data point.Numerical experience shows that our algorithm is better than many of others,including the famous B R algorithm.     

MILP approach to pattern generation in logical analysis of data

Pattern generation methods for the Logical Analysis of Data (LAD) have been term-enumerative in nature. In this paper, we present a Mixed 0-1 Integer and Linear Programming (MILP) approach that can identify LAD patterns that are optimal with respect to various previously studied and new pattern selection preferences. Via art of formulation, the MILP-based method can generate optimal patterns that also satisfy user-specified requirements on prevalence, homogeneity and complexity. Considering that MILP problems with hundreds of 0-1 variables are easily solved nowadays, the proposed method presents an efficient way of generating useful patterns for LAD. With extensive experiments on benchmark datasets, we demonstrate the utility of the MILP-based pattern generation.     

多状态系统的LAD决策树的建树方法研究

LAD( Logistic Data Analysis Tree)是一种逻辑数据分析技术 ,它将布尔代数和优化分析方法引入到了判别分析领域 ,提出了一种布尔变量集合的变量筛选和建模方法 ,并可以对冗余模式进行可视化识别与删除 .但目前的 LAD技术还仅限于二状态 ,而且算法复杂 .本文将 LAD决策树推广到了多状态情形 ,以三状态下建立 LAD决策树为例 ,提出了不可分辨度的定义 ,并以其下降最大作为寻找最优决策树的依据 .说明多状态下建立 LAD决策树的计算方法及重要的算法步骤 .最后 ,本文以鄱阳湖地区洪涝灾害影响研究为案例 ,采用 LAD决策树方法对其进行判别分析 .     

Maximum patterns in datasets

Given a binary dataset of positive and negative observations, a positive (negative) pattern is a subcube having a nonempty intersection with the positive (negative) subset of the dataset, and an empty intersection with the negative (positive) subset of the dataset. Patterns are the key building blocks in Logical Analysis of Data (LAD), and are an essential tool in identifying the positive or negative nature of “new” observations covered by them. We develop exact and heuristic algorithms for constructing a pattern of maximum coverage which includes a given point. It is shown that the heuristically constructed patterns can achieve 81-98% of the maximum possible coverage, while requiring only a fraction of the computing time of the exact algorithm. Maximum patterns are shown to be useful for constructing highly accurate LAD classification models. In comparisons with the commonly used machine learning algorithms implemented in the publicly available Weka software package, the implementation of LAD using maximum patterns is shown to be a highly competitive classification method.     

Empirical likelihood for AR-ARCH models based on LAD estimation

By employing the empirical likelihood method,confidence regions for the stationary AR(p)-ARCH(q) models are constructed.A self-weighted LAD estimator is proposed under weak moment conditions.An empirical log-likelihood ratio statistic is derived and its asymptotic distribution is obtained.Simulation studies show that the performance of empirical likelihood method is better than that of normal approximation of the LAD estimator in terms of the coverage accuracy,especially for relative small size of observation.     

Strong valid inequalities for Boolean logical pattern generation

0–1 multilinear programming (MP) captures the essence of pattern generation in logical analysis of data (LAD). This paper utilizes graph theoretic analysis of data to discover useful neighborhood properties among data for data reduction and multi-term linearization of the common constraint of an MP pattern generation model in a small number of stronger valid inequalities. This means that, with a systematic way to more efficiently generating Boolean logical patterns, LAD can be used for more effective analysis of data in practice. Mathematical properties and the utility of the new valid inequalities are illustrated on small examples and demonstrated through extensive experiments on 12 real-life data mining datasets.