基于灰色理论的线性回归模型的参数理论及应用

线性回归分析是数理统计学的基本内容之一,但传统数理统计学中的线性回归分析,是建立在非模糊的随机数据上的线性回归估计和回归系数检验。而现实经济社会中大量存在含有模糊或灰色等不分明性的数据,面对这类不分明性数据,简单地使用传统的统计分析方法显然是不足取的。要想较为科学合理地分析与决策,需要利用灰色系统的相关理论,应用于随机系统信息,从而建立灰色线性回归估计、预测和灰色回归系数检验的基本理论方法,并把该方法应用于金融分析实例中,与经典线性回归分析方法进行对比,足见灰色线性回归方法能够提供比经典线性回归较多的有效信息,从而提出处理不分明数据新的方法。     

基于纵向数据的半参数变系数部分线性回归模型

纵向数据是数理统计研究中的复杂数据类型之一0,在生物、医学和经济学中具有广泛的应用．在实际中经常需要对纵向数据进行统计分析和建模．文章讨论了纵向数据下的半参数变系数部分线性回归模型,这里的纵向数据的在纵向观察在时间上可以是不均等的,也可看成是按某一随机过程来发生．所研究的半参数变系数模型包括了许多半参数模型,比如部分线性模型和变系数模型等．利用计数过程理论和局部线性回归方法,对于纵向数据下半参数变系数进行了统计推断,给出了参数分量和非参数分量的profile最小二乘估计,研究了这些估计的渐近性质,获得这些估计的相合性和渐近正态性．     

居民收入和消费预测的灰理论方法

阐述灰色模型GM(1,1)建立及检验的基本理论和方法.并依据2000年—2005年浙江农村居民人均纯收入和人均生活消费数据,利用GM(1,1)模型建模方法,对“十一五”期间浙江农民的纯收入和生活消费进行了预测.     

基于灰色系统理论的多元线性回归分析

运用灰色系统理论剔除了自变量观察数据中的噪声污染,对传统的多元线性回归分析方法进行了改进,建立了灰色多元线性回归分析模型.将模型应用于陕西省就业问题的研究,取得了满意的预测效果.     

关于两总体均值差的一种半参数假设检验方法

近年来, 已有一些在半参数密度函数比模型下建立半参数统计分析方法的报道, 这些方法往往比参数方法稳健, 比非参数方法有效. 在本文里, 我们提出一种半参数的假设检验方法用于对两总体均值差进行假设检验. 该方法主要建立在对两总体均值差进行半参数估计的基础上. 我们报告了一些理论和统计模拟的结果, 得出该方法在数据符合正态性假设时, 比常用的参数和非参数方法略好; 而在数据不符合正态性假设时, 它的优势就非常明显. 我们还将提出的方法用到了两组真实数据的分析上.     

奇异线性模型的线性假设检验问题

本文研究奇异线性模型的假设检验问题，我们用初等直接的方法了根据最小二乘统一理论所构造的检验统计量服从Ｆ分布，并给出了这些结果在ｐａｎｅｌ数据模型。两级抽样回归模型以及不完全数据回归模型中的应用。     

基于纵向数据与生存时间数据联合建模的变量选择

纵向数据和生存时间数据联合建模能减少由单独建模所引起的偏差,本文研究了基于纵向数据和生存时间联合建模的变量选择问题。对于生存时间数据,把生存时间做离散化处理,引入离散风险函数的Probit模型;对于纵向数据,利用线性混合效应模型建模。采用共享随机效应的方法对纵向数据和生存时间进行联合建模,通过利用多元高斯隐截断分布,构造出联合模型的精确似然。然后对似然函数加惩罚,重新构造目标函数,得到回归系数的稀疏估计量。理论证明以及数值模拟研究展示了稀疏估计量的良好性质。     

论灰色理论的三数据建模

本文通过论证序列的GM(1,1)模型计算值与原始序列的初值无关,讨论仅有三个数据构成的序列的灰色建模问题,得出可进行灰色建模的最少数据数为3的结论.     

基于线性样条的门限随机波动率模型及其实证研究

为了刻画金融领域中资产收益的条件均值和波动率的双重非对称性特征,本文基于线性样条的方法提出一种新的门限随机波动率模型(LPTSV),它可以根据到达市场消息的大小和方向来同时描述这两种非对称性情况,可以很好地对资产收益及其波动率进行建模。利用R2WinBUGS软件包对LPTSV模型进行了贝叶斯参数估计。模拟实验说明贝叶斯分析在LPTSV模型的参数估计方面是有效的。最后利用LPTSV模型为上证综合指数和深证成份指数日收益率数据进行了实证分析。描述性统计分析和参数估计的结果均表明:利用LPTSV模型对以上两组数据进行建模是合理的。本文为资产收益和波动率之间的实证关系研究提供了一定的启示。     

基于灰色马尔科夫链预测模型的广西边境小额贸易预测研究——灰色系统理论应用系列论文之三

在分析广西边境小额贸易现状的基础上,运用灰色模型和马尔科夫链的基本理论,构建灰色马尔科夫模型进行了预测.结果表明,经过二阶弱化处理、灰色建模、灰色新陈代谢以及灰色马尔科夫预测的结果,能明显地提高预测精度.最后,提出了加大基础设施建设、转变边贸流通模式、构建沿边型产业开放体系、提高边境贸易便利化水平和培育发展边境特色经济带等对策建议.     

苎麻纤维细度测试与分析的灰色模型

基于灰色系统理论的灰色建模应用于试验数据的相关分析 ,比基于数理统计的回归分析在实际应用中由于所需样本容量较小而具有明显的优点 ,特别对贫信息系统适用 .从而可避免在回归分析中因样本容量太小而致使回归方程的误差不可预测的弊端 .鉴于上述原理 ,本文采用灰色系统理论建立了苎麻纤维Tex数 Y与投影宽度 X之间的灰色 GM( 1 ,2 )模型 ,并进行了误差分析 .利用此模型探索了通过测定苎麻纤维投影宽度来计算其 Tex数的方法 .为生产工艺控制、产品质量检验和监督提供了一种简便而科学的办法 .     

渗流问题灰色数值模型的解法研究

灰色数值模型的求解是研究灰色数值模型的一个重要问题 .本文根据灰集合、灰数及其灰色运算规则 ,在渗流系统的基本灰色数值模型的基础上 ,分析了求解这类模型的一整套灰色数值算法 ,并对灰色数值算法、普通算法和经典数值方法的计算结果进行了全面比较 ,论证了灰色数值算法对灰信息传递的正确性和对渗流系统描述的合理性 .     

Reviews on the Research of Dynamic Mortality Models

Mortality forecasting is the basis of population forecasting. In recent years, new progress has been made in mortality models. From the earliest static mortality models, mortality models have been developed into dynamic forecasting models including time terms, such as Lee-Carter model family, CBD model family and so on. This paper reviews and sorts out relevant literature on mortality forecasting models. With the development of dynamic models, some scholars have developed a series of mortality improvement models based on the level of mortality improvement. In addition, with the progress of mortality research, multi-population mortality modeling attracted the attention of researchers, and the multi-population forecasting models have been constantly developed and improved, which play an important role in the mortality forecasting. With the continuous enrichment and innovation of mortality model research methods, new statistical methods (such as machine learning) have been applied in mortality modeling, and the accuracy of fitting and prediction has been improved. In addition to the extension of classical modeling methods, issues such as small-area population or missing data of the population, the elderly population, the related population mortality modeling are still worth studying.     

Environmental data modeling

In the statistical analysis of environmental data, space and time are often disregarded by the use of classical methods such as hydrological analysis of frequencies or factor analysis. But these methods, based on the assumptions of independent identically distributed observations, cannot be efficient. This article discusses more appropriate approaches regarding the space and time influences, and surveys some important proposals of modeling environmental data. Three examples show the workability of the presented theory. Within the first example, a system to detect abnormal occurrences in water quality as early as possible depending in quasi-continuous data is developed. A second example decomposes a water quality time series into three unobservable components. Finally, it is shown how the factor model can be extended to time series data.     

Rolling element bearing diagnosis based on probability box theory

Feature extraction leads to the loss of statistical information of raw data and ignores the sampling uncertainty and the fluctuations in the signal over time in mechanical fault diagnosis. In this paper, novel modeling methods for mechanical signals based on probability box theory were proposed to solve the above problem. First, the type of random distribution of the bearing signals were analyzed. Then, a Dempster-Shafer structure was obtained to establish a probability box model. To address the identification difficulty of the type of random distribution for the bearing signals, a second probability box model was established based on a vector consisting of features from the bearing signals. If the data are not found to follow a random distribution, a third modeling method based on the definition of probability boxes was proposed. The effectiveness and applicability of the three proposed models were compared with experimental data from rolling element bearings. The combination of probability box theory and mechanical fault diagnosis theory can open up a new research direction for mechanical fault diagnosis.     

A normal hierarchical model and minimum contrast estimation for random intervals

Many statistical data are imprecise due to factors such as measurement errors, computation errors, and lack of information. In such cases, data are better represented by intervals rather than by single numbers. Existing methods for analyzing interval-valued data include regressions in the metric space of intervals and symbolic data analysis, the latter being proposed in a more general setting. However, there has been a lack of literature on the parametric modeling and distribution-based inferences for interval-valued data. In an attempt to fill this gap, we extend the concept of normality for random sets by Lyashenko and propose a Normal hierarchical model for random intervals. In addition, we develop a minimum contrast estimator (MCE) for the model parameters, which is both consistent and asymptotically normal. Simulation studies support our theoretical findings and show very promising results. Finally, we successfully apply our model and MCE to a real data set.     

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??Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.     

基于统一灰色生成算子的三参数离散灰色预测模型及其应用

现有三参数离散灰色预测模型的累加阶数取值范围局限于正实数,导致模型建模能力和作用空间受限。为此,论文首先引入实数域统一灰色生成算子;然后,基于统一灰色生成算子构造了新型三参数离散灰色预测模型,实现了其阶数从正实数到全体实数的拓展与优化,从而使得新型模型具备挖掘时序数据积分特性与差异信息的双重功能;最后,将该新模型应用于某装甲装备维修经费的建模,结果显示其精度优于其它同类灰色模型。本研究成果对完善灰色算子基础理论及提高灰色预测模型建模能力具有重要价值。     

Maximum Likelihood Estimation of Hidden Markov Multivariate Normal Distribution Parameters

Hidden Markov model is widely used in statistical modeling of time, space and state transition data. The definition of hidden Markov multivariate normal distribution is given. The principle of using cluster analysis to determine the hidden state of observed variables is introduced. The maximum likelihood estimator of the unknown parameters in the model is derived. The simulated observation data set is used to test the estimation effect and stability of the method. The characteristic is simple classical statistical inference such as cluster analysis and maximum likelihood estimation. The method solves the parameter estimation problem of complex statistical models.