小波分析在管理数据处理中的应用

提出了一种基于小波变换的管理数据处理方法，把公司管理上的数据看成一个非平稳的时间序列，利用小渡函数将该时间序列分解到不同的频率通道上，然后将分解后的信号当作近似的平稳时间序列，用一些传统的统计方法进行预测，同时对中国足球彩票若干期的销售量数据进行了处理和预测，并将结果与实际销量以及用传统的AR模型的预测值进行了比较。     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

三螺旋创新模式的理论探讨

基于非线性网状创新模型提出的“三螺旋场”和“三螺旋循环”概念进一步推进了三螺旋创新模式的理论研究。三螺旋场概念旨在解释在大学、产业和政府三股螺旋之间存在的相对独立和彼此作用的本质，说明三螺旋的生成原理、静态表现和动态演化特征。三螺旋的生成原理在于创新过程的非线性本质和多主体特征，静态表现为“内核外场模型”，而动态演化过程则在于纵向进化和横向循环。发生在三股螺旋之间的三螺旋循环揭示了在大学、产业和政府之间以人员、信息和产品流动为特征的相互作用和运行机制。     

再论科技进步与社会发展之间的非线性关系

流行的观点认为,科技进步与社会发展二者之间具有相互肯定的对应关系,即社会发展的历史就是科技进步的历史,科技进步必然导致社会发展,科技越进步,社会越发展,科技每前进一步,社会就相应地发展一步。本文通过对传统的社会发展理念与科技进步的负面效应进行分析,批判了这种对社会发展与科技进步二者之间的关系只作线性把握的局限,指出在科技进步与社会发展之间存在着极其复杂的非线性关系。     

基于视觉模型的双正交小波图像水印算法

提出了一种基于人类视觉系统模型的双正交小波多分辨图像水印算法,该算法充分利用小波多分辨的优点及人眼视觉系统的特性,保证了水印的不可见性及鲁棒性,同时在检测水印时也不需要原始图像,仅需涉及到相关的几个细节子图。实验表明该水印算法对于中值滤波、叠加加性噪声、JPEG有损压缩三种图像处理都是鲁棒的。检测算法还有计算量小,检测速度快的特点。     

Generalized Leverage and its Applications

The generalized leverage of an estimator is defined in regression models as a measure of the importance of individual observations. We derive a simple but powerful result, developing an explicit expression for leverage in a general M -estimation problem, of which the maximum likelihood problems are special cases. A variety of applications are considered, most notably to the exponential family non-linear models. The relationship between leverage and local influence is also discussed. Numerical examples are given to illustrate our results     

化学反应中的非线性现象

本文以“水中花园”和“化学振荡”等实验事实,论述了化学反应中的自然分形和自组织过程等非线性现象.     

Correlated random effects regression analysis for a log-normally distributed variable

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.     

Causal structure among US corn futures and regional cash prices in the time and frequency domain

This study investigates causal structure among daily Chicago Board of Trade corn futures prices and seven regional cash series from Iowa, Illinois, Indiana, Ohio, Minnesota, Nebraska, and Kansas for January 2006–March 2011. Their wavelet transformed series are further analyzed for causal relationships at different time scales. Empirical results indicate no causality among states or between the futures and a cash series for time scales shorter than one month. As scales increase but do not exceed a year, bidirectional causal flows are determined among all prices. The information leadership role of the futures against a cash price is identified for the scale longer than one year and raw series, at which no interstate causality is found.     

Double shrinkage estimators for large sparse covariance matrices

Covariance matrices play an important role in many multivariate techniques and hence a good covariance estimation is crucial in this kind of analysis. In many applications a sparse covariance matrix is expected due to the nature of the data or for simple interpretation. Hard thresholding, soft thresholding, and generalized thresholding were therefore developed to this end. However, these estimators do not always yield well-conditioned covariance estimates. To have sparse and well-conditioned estimates, we propose doubly shrinkage estimators: shrinking small covariances towards zero and then shrinking covariance matrix towards a diagonal matrix. Additionally, a richness index is defined to evaluate how rich a covariance matrix is. According to our simulations, the richness index serves as a good indicator to choose relevant covariance estimator.