关于假设检验中显著性水平的选择

假设检验是质量管理和控制中广泛应用的一种统计推断方法.但是,我们知道根据样本提供的信息对总体的参数或分布进行假设检验,可能导致两类错误:第一类错误是如果零假设H0事实上是正确的,而根据样本信息计算的检验统计量却落在否定区,从而我们错误地拒绝了零假设,这叫以真为假;第二类错误是零假设H0事实上是错误的,而根据样本信息计算的检验统计量落在肯定区,从而使我们错误地接受了零假设,这叫以假乱真.以样本平均数的分布为例,假设检验中造成这两类错误的概率大小关系,可通过下图来说明: 图中分布1,分布2的方差σ2是一样的,对样本平均数假…     

多元时间序列GARCH型模型的诊断检验

多元时间序列GARCH型模型已被证实在理论和实际中具有重要作用.该文对这一类模型的拟合优度提出了一组得分型检验统计量.这些检验在零假设模型下渐近服从卡方分布,计算简单,临界值容易得到.检验对备择模型比较敏感,能侦察到以1/n~(1/2)的速度收敛到零假设的备择模型.对于可能的多个备择,构造了渐近分布自由的Maximin检验;而对于饱和备择情形,基于得分型检验的思想提出了一个构造Omnibus检验的可能性.值得指出的是构造的这组检验能检测到零假设模型的条件协差阵的每一部分可能的偏离,从而当模型被错误指定时,该检验能提供相关信息进行模型修正.模拟结果表明该文的检验表现理想.     

基于随机矩阵理论的高维数据球形检验

本文基于随机矩阵理论,研究了一般总体的高维协方差矩阵的球形检验.当样本量小于数据维数时,经典的似然比检验方法在球形检验中已无法使用.通过引入样本协方差矩阵谱分布的高阶矩,构造出一个新的检验统计量,并给出其在零假设下的渐近分布.模拟实验表明所提出的统计量在控制第一类错误概率的基础上能有效提高检验功效,对于Spiked模型效果尤为显著.     

基于病例队列数据的比例风险模型的诊断

病例队列设计是一种在生存分析中广泛应用的可以降低成本又能提高效率的抽样方法.对于病例队列数据,已经有很多统计方法基于比例风险模型来估计协变量对生存时间的影响.然而,很少有工作基于病例队列数据来检验模型的假设是否成立.在这篇文章中,我们基于渐近的零均的值随机过程提出了一类检验统计量,这类检验统计量可以基于病例队列数据来检验比例风险模型的假设是否成立.我们通过重抽样的方法来逼近上述检验统计量的渐近分布,通过数值模拟来研究所提方法在有限样本下的表现,最后将所提出的方法应用于一个国家肾母细胞瘤研究的真实数据集上.     

最小一乘估计在多重检验中的应用——基于乳腺癌微阵列数据

运用多重检验方法对高维数据进行推断统计分析.首先将最小一乘估计算法应用在多重检验分析中,构造出新的估计真实零假设个数的方法.其次对最小一乘与最小二乘方法估计真实零假设个数的准确性进行模拟比较分析,模拟结果表明前者较后者估算结果更准确.最后,将上述估计方法应用于乳腺癌微阵列数据的分析中寻找有表达差异的基因.检验结果共找到118个差异基因,其中85个基因在生物学上是有效基因,实证表明该方法具有一定的实用性.     

预测回归模型序列相关性的Jackknife经验似然比检验

预测回归模型是计量经济学中的重要模型,而相关的序列检验问题在文献中尚未被提及.考虑到序列相关性检验在模型实证中的重要性,文章基于Jackknife经验似然法,构造了该模型的序列相关检验统计量,并在一定条件下推导了零假设成立时检验统计量的渐近分布,分析了它在局部备择假设下的功效情况,最后通过随机模拟和实际数据例子验证了该检验方法的有限样本性质.     

具有随机删失数据的部分线性模型的拟合优度检验的渐近性质

研究随机删失部分线性回归模型的假设检验问题. 提出了一个检验统计量来检验数据是否满足一个部分线性回归模型, 它是基于残差的cusum过程的平方形式. 研究了零假设下和局部对立假设下检验统计量的渐近分布. 数值模拟表明该检验方法有好的检验功效.     

太阳辐射时间序列的非线性检验

检验太阳辐射时间序列是否有非线性特征,对于分析、建模和预测太阳辐射量是重要、有益的.提出用基于替代数据的检验方法来检验太阳辐射时间序列是否存在非线性特征,并将数据序列的三阶矩作为检验统计量.选取了美国Montana州Dillon地区和Wyoming州Green Rivet地区每日总辐射量、Utah州Moab地区的每月日平均总辐射量时间序列作为检验对象.数值分析的统计结果表明所研究的日总辐射时间序列存在非线性,而每月日平均总辐射时间序列未检测出非线性.因而,对太阳辐射时间序列建模和预测之前,检验其是否有非线性特征是必要的.     

基于神经网络的期货预测数据预处理问题研究

期货预测研究在期货价格数据预处理和预测方法上存在直接套用原始数据代入模型以及价格预测模型和原始数据模型不相匹配等问题,需要予以解决.本研究在采用通货膨胀率指数调整、平均周期项以及滤波等方法对铜期货价格时间序列数据进行预处理后,分别将预处理前后的期货价格数据输入到神经网络预测模型,通过比较两者预测结果来验证原始期货时间序列数据预处理的必要性.     

线性常微分方程参数稳定性的统计推断

对具有随机误差的观测数据, 讨论了常系数线性常微分方程参数稳定性的统计推断问题. 通过残差项的Karhunen-Loeve 分解, 给出了变点检验步骤及其在原假设下的极限分布. 在对立假设下定义了变点的估计, 证明了检验以及估计的一致性. 对常系数二阶常微分方程进行了统计模拟, 结果表明原假设下的极限分布是对真实分布非常好的近似; 对立假设下, 即使输入函数的频率存在0.75% 的变化, 上述检验也能以大概率拒绝原假设. 最后利用上述方法研究了英国中部地区的气温数据, 揭示了数据一些新的特点.     

Finite-size effect and the components of multifractality in financial volatility

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has an impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.     

小波分析方法在金融股票数据预测中的应用

利用小波分析预测方法对金融数据—股票收盘价这一典型的非平稳时间序列进行预测.使用M a llat小波分解算法对数据进行分解,对分解后的数据进行平滑处理,然后再进行重构,而重构之后的数据就成为近似意义的平稳时间序列,这样就得到了原始数据的近似信号,再应用传统时间序列预测方法对重构后的数据进行预测,将预测结果与实际值,以及和传统预测方法预测结果比较,小波分析方法预测效果更为理想.     

PSO with surrogate models for feature selection: static and dynamic clustering-based methods

Feature selection is an important but often expensive process, especially with a large number of instances. This problem can be addressed by using a small training set, i.e. a surrogate set. In this work, we propose to use a hierarchical clustering method to build various surrogate sets, which allows to analyze the effect of surrogate sets with different qualities and quantities on the feature subsets. Further, a dynamic surrogate model is proposed to automatically adjust surrogate sets for different datasets. Based on this idea, a feature selection system is developed using particle swarm optimization as the search mechanism. The experiments show that the hierarchical clustering method can build better surrogate sets to reduce the computational time, improve the feature selection performance, and alleviate overfitting. The dynamic method can automatically choose suitable surrogate sets to further improve the classification accuracy.     

Interactive Visualization of Hierarchically Structured Data

We introduce methods for visualization of data structured along trees, especially hierarchically structured collections of time series. To this end, we identify questions that often emerge when working with hierarchical data and provide an R package to simplify their investigation. Our key contribution is the adaptation of the visualization principles of focus-plus-context and linking to the study of tree-structured data. Our motivating application is to the analysis of bacterial time series, where an evolutionary tree relating bacteria is available a priori. However, we have identified common problem types where, if a tree is not directly available, it can be constructed from data and then studied using our techniques. We perform detailed case studies to describe the alternative use cases, interpretations, and utility of the proposed visualization methods.     

Multi-step prediction of time series with random missing data

Multi-step prediction is still an open challenge in time series prediction. Moreover, practical observations are often incomplete because of sensor failure or outliers causing missing data. Therefore, it is very important to carry out research on multi-step prediction of time series with random missing data. Based on nonlinear filters and multilayer perceptron artificial neural networks (ANNs), one novel approach for multi-step prediction of time series with random missing data is proposed in the study. With the basis of original nonlinear filters which do not consider the missing data, first we obtain the generalized nonlinear filters by using a sequence of independent Bernoulli random variables to model random interruptions. Then the multi-step prediction model of time series with random missing data, which can be fit for the online training of generalized nonlinear filters, is established by using the ANN’s weights to present the state vector and the ANN’s outputs to present the observation equation. The performance between the original nonlinear filters based ANN model for multi-step prediction of time series with missing data and the generalized nonlinear filters based ANN model for multi-step prediction of time series with missing data is compared. Numerical results have demonstrated that the generalized nonlinear filters based ANN are proportionally superior to the original nonlinear filters based ANN for multi-step prediction of time series with missing data.     

Detection of low-dimensional chaos in buildings energy consumption time series

In this paper, nonlinear time series modeling techniques are applied to analyze building energy consumption data. The time series were obtained for the benchmark data set Proben 1, and comes from the first energy prediction contest, the Great Building Energy Predictor Shootout I, organized by ASHRAE. The phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem suggested by TAKENS. The embedding parameters, e.g. the delay time and the embedding dimension are estimated using the average mutual information (AMI) of the data and the false nearest neighbor (FNN) algorithm, respectively. Nonlinearity was detected, by applying the surrogate data sets method.Numerically estimated non-integral fractal dimension and a positive Lyapunov exponent are not necessarily sufficient indication of chaos; therefore we apply a more stringent criterion, developed by Gao and Zheng, which is based on the logarithmic displacement of time-dependent exponent curves, and show that these data are chaotic.Based on this analysis and proof, we then calculate the correlation dimension of the resulting attractor and the largest Lyapunov exponent. The correlation dimension 3.47 and largest Lyapunov exponent 0.047 are estimated. These results indicate that chaotic characteristics obviously exist in the specific energy consumption data set, and thus techniques based on phase space dynamics can be used to analyze and predict buildings energy use.     

Motif detection inspired by immune memory

The search for patterns or motifs in data represents an area of key interest to many researchers. In this paper we present the motif tracking algorithm (MTA), a novel immune-inspired pattern identification tool that is able to identify variable length unknown motifs that repeat within time series data. The algorithm searches from a neutral perspective that is independent of the data being analysed and the underlying motifs. In this paper we test the flexibility of the MTA by applying it to the search for patterns in two industrial data sets. The algorithm is able to identify a population of meaningful motifs in both cases, and the value of these motifs is discussed.     

季节性数据的横断面建模方法

本文提出了一种对季节性数据建立数学模型的新方法──横断面方法．其思想是，把一个季节性时间序列划分成为数相当于一个季节周期长度的若干个子序列，在这些子序列中已完全消除了季节性因素，然后对这些子序列分别建立形式各异的数学模型，最后再把这些子序列的数学模型综合起来就得到了对原始序列的数学模型．     

Drift Estimation of Multiscale Diffusions Based on Filtered Data

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coefficient of the homogenized equation requires pre-processing of the data, often in the form of subsampling; this is because the two-scale equation and the homogenized single-scale equation are incompatible at small scales, generating mutually singular measures on the path space. We avoid subsampling and work instead with filtered data, found by application of an appropriate kernel function, and compute maximum likelihood estimators based on the filtered process. We show that the estimators we propose are asymptotically unbiased and demonstrate numerically the advantages of our method with respect to subsampling. Finally, we show how our filtered data methodology can be combined with Bayesian techniques and provide a full uncertainty quantification of the inference procedure.