可线性化的含T—Fuzzy数据的非线性回归预测模型

本文探讨了一类可化为线性回归问题的含T—Fuzzy数据的非线性回归预测模型。首先,用两种途经将这类模型化为确定型,并论证了这两种化法的等价性。其次,采取fuzzy加权处理,避免了因线性化而产生的误差。最后由确立经变换得到的经典模型,从而确立原含T—Fuzzy数据的非线性预测模型。用相同的方法,先确定含T—Fuzzy数据的非线性回归预测模型,再确定非线性自回归问题。     

拟线性回归预测模型的稳定最小二乘解

可线性化回归预测模型通过换元进行线性回归,换元前后的因变量具有异方差性,致使拟线性回归参数的精度较低.运用GL算法给出了此类模型的稳定最小二乘解,提高了参数的估计精度,最后给出了一个应用实例.     

可线性化的非线性回归的有关问题与几种回归方法的比较

对于幂函数、指数函数等类型的非线性回归,只当采用乘积随机误差时才能够线性化.导出了采用乘积随机误差时幂函数型因变量的数学期望的表达式,表明因变量的估计值并非是其数学期望的估值;导出了非线性回归与其线性化回归二者的残差平方和之间的关系式,表明当对非线性回归的因变量做了变换时,传统方法所求非线性回归系数不满足该因变量的残差平方和为最小.故幂函数、指数函数等类型的回归计算,应采用非线性回归方法求解.实例进一步表明,非线性回归方法高斯-牛顿法和麦夸尔特法均显著优于传统方法,且借助MATLAB软件易于实现.     

北京非典型肺炎数学模型

探讨了北京非典型肺炎数学模型 ,利用动力学和非线性回归方法建立了北京非典型肺炎预测模型 .     

应用SAS解非线性回归问题

.应用SAS/STAT估计非线性回归模型中的参数.首先,通过变量代换,把可以线性化的非线性回归模型化为线性回归模型,并用普通最小二乘法、主成分分析法和偏最小二乘法求模型中的参数和回归模型.其次,通过改良的高斯—牛顿迭代法来估计Logistic模型和Compertz模型中的参数.     

指数函数与幂函数回归计算的极大似然法及其应用

为提高拟合精度,研究了指数函数与幂函数非线性回归计算的极大似然法.分析表明,在指数函数与幂函数回归计算的因变量为正态随机变量的情况下,极大似然估计与非线性回归的最小二乘估计具有相同的结果;导出了极大似然法求解指数函数与幂函数回归参数的方程式,并给出了计算方法.此方法拟合因变量的残差平方和为最小.实例表明,本文方法拟合精度与高斯-牛顿法相当、显著优于线性化的回归方法,而计算方法要比高斯-牛顿法简单方便,易于实现.     

非线性系统的输出反馈完全线性化

一、引言近年来,用微分几何的方法讨论非线性系统的精确线性化问题,在国内外文献中均有较多讨论.目前的讨论较多集中于状态方程的反馈线性化.但对于实际应用,状态方程与输出方程同时线性化的问题往往更为重要.这类问题可严格叙述为     

非零截距线性和非线性回归模型的T-型稳健估计算法

首先给出非零截距线性模型T-型估计的模型与EM算法,其次给出非线性回归模型参数的T-型估计,利用泰勒级数对模型线性化,得到参数估计的迭代算法,最后用数值模拟实验验证了该算法的正确性和证实了T-型估计的稳健性.     

非线性回归模型校正和应用

本文提出了非线性回归模型的校正模型，该方法尤其适于当社会经济系统发生变化时供建立预测模型之用，从而扩大了非线性回归模型的应用范围。经实例验证，该方法的效果是显著的。     

耦合AF-SVR的短时交通流量预测模型

交通流量预测是城市智能交通系统的重要研究内容之一,是缓解城市拥堵、实现智能交通管理和建设智慧城市的前提,基于短时交通流量的复杂性及非线性等特点,提出耦合AF-SVR的短时交通流量预测模型.模型结合了鱼群算法较好的并行搜索性能和支持向量回归机较好的非线性拟合能力,利用该模型对短时交通流量数据进行仿真实验,结果表明:模型较BP神经网络预测模型具有较高的预测精度,是短时交通流预测的一种有效方法.     

Parametric regression analysis of imprecise and uncertain data in the fuzzy belief function framework

In this paper, parametric regression analyses including both linear and nonlinear regressions are investigated in the case of imprecise and uncertain data, represented by a fuzzy belief function. The parameters in both the linear and nonlinear regression models are estimated using the fuzzy evidential EM algorithm, a straightforward fuzzy version of the evidential EM algorithm. The nonlinear regression model is derived by introducing a kernel function into the proposed linear regression model. An unreliable sensor experiment is designed to evaluate the performance of the proposed linear and nonlinear parametric regression methods, called parametric evidential regression (PEVREG) models. The experimental results demonstrate the high prediction accuracy of the PEVREG models in regressions with crisp inputs and a fuzzy belief function as output.     

Robust kernel ridge regression based on M-estimation

Ridge regression (RR) and kernel ridge regression (KRR) are important tools to avoid the effects of multicollinearity. However, the predictions of RR and KRR become inappropriate for use in regression models when data are contaminated by outliers. In this paper, we propose an algorithm to obtain a nonlinear robust prediction without specifying a nonlinear model in advance. We combine M-estimation and kernel ridge regression to obtain the nonlinear prediction. Then, we compare the proposed method with some other methods.     

A mathematical programming approach to clusterwise regression model and its extensions

The clusterwise regression model is used to perform cluster analysis within a regression framework. While the traditional regression model assumes the regression coefficient (β) to be identical for all subjects in the sample, the clusterwise regression model allows β to vary with subjects of different clusters. Since the cluster membership is unknown, the estimation of the clusterwise regression is a tough combinatorial optimization problem. In this research, we propose a “Generalized Clusterwise Regression Model” which is formulated as a mathematical programming (MP) problem. A nonlinear programming procedure (with linear constraints) is proposed to solve the combinatorial problem and to estimate the cluster membership and β simultaneously. Moreover, by integrating the cluster analysis with the discriminant analysis, a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis. The cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model.     

On the use of kernel-based methods in sound synthesis by physical modeling

In this paper we discuss an approach to the modeling of acoustic systems that combines prior information, exploited through physical modeling, and nonlinear dynamics reconstruction, exploited through support vector machine regression. We demonstrate our approach on two case studies, both addressing the broad class of acoustic systems for which the sound generation is obtained through the interaction of a linear system (resonator) and a nonlinear system (excitation). The first case is a physically based impact model, where the resonator is described in terms of its normal modes and the nonlinear contact force is modeled through a simplified collision equation and kernel regression. In the second case study, a model of the voice phonation is illustrated in which the vocal folds are represented by a lumped linear mass-spring system and the nonlinear flow component is modeled through simple Bernoulli-based equations and kernel regression.     

基于多目标规划法的模糊线性回归分析

讨论输入、输出均为模糊数,回归系数为实数时的模糊线性回归分析。由于模糊最小二乘线性回归容易受异常值的影响,而最小一乘法能有效地降低回归模型的误差。为此,基于最小一乘法,建立多目标规划模型并将其转化为非线性规划问题进行求解,从而实现模糊线性回归模型的参数估计。最后,结合一个数值实例,验证和比较该方法的合理性和优越性。     

基于pena距离的非线性回归模型的影响分析

基于pena距离统计量对非线性回归模型的影响分析进行了讨论,得到了非线性回归模型的pena距离公式,并对公式的分析性质以及其对高杠异常点的检测作用做出了相应的结论,得出了在一定条件下pena距离对异常点的检测优于Cook距离的结论,特别是对高杠杆异常点的检验,pena距离的效果更加明显,给出了实际数据检验结果,对方法的有效性进行了验证。     

非线性再生散度模型的Bayes估计

非线性再生散度模型是指数族非线性模型、广义线性模型和正态非线性回归模型的推广和发展,唐年胜等人研究了该模型参数的极大似然估计及其统计诊断。本文基于Gibbs抽样和MH抽样算法讨论非线性再生散度模型参数的Bayes估计。模拟研究和实例分析被用来说明该方法的有效性。     

Asymptotic efficient estimation in semiparametric nonlinear regression models

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