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。     

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.     

一般进化的微观机制

一般进化在系统内微观子系统层次上的微观机制 ,是涨落单元内外部子系统之间互为因果循环的正反馈类型的相互作用。其本质特征 ,是双方之间作用的非对称性 ,表现为一方的属性支配着另一方属性的变化 ,另一方丧失自己原先的属性而以一方的属性为自己的新属性。这种相互作用同时具有协同和放大效应 ,从而使涨落单元由局部迅速放大到整体 ,而形成一个新的有序结构     

General m-esttmators and applications to bounded influence estimation for non-linear regression

In this paper, we study the M-estimators in the case that λ_F:(β)=E_F:(φ(Z,β))=0 has more than one solution, We show that the numerical iterative procedures converge and that the resulting estimators are consistent and asymptotically normal. We apply them to the non-linear regression models, and then, we find an optimal M-estimate among those that have bounded gross error sensitivity.     

意境的时空结构和审美功能系统

意境作为中国传统美学的重要范畴和艺术至境,是由时间关系和空间关系之间的联系所构成的独特时空体,它凝结着国人的审美理想和生存智慧.意境是一个完整的结构整体,是时间与空间的艺术整合,是传统言意论与意象论思想的融合和升华.这一结构作为基础制约着其中各个审美要素及相互关系,也使其诗学功能的发挥呈现出系统性.在意境阐释中,系统论思想方法仍是有效的理论利器,而对意境中时间性含蕴的发掘当是关键所在.     

Semiparametric Regression Smoothing of Non-linear Time Series

In this paper, we consider using a semiparametric regression approach to modelling non-linear autoregressive time series. Based on a finite series approximation to non-parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey–Glass system is presented to support the large sample study.