Quasi-minimax estimation in the general linear regression model

This paper is mainly concerned with minimax estimation in the general linear regression model y=Xβ+ε$y=X\beta +\epsilon$ under ellipsoidal restrictions on the parameter space and quadratic loss function. We confine ourselves to estimators that are linear in the response vector y  . The minimax estimators of the regression coefficient β$\beta$ are derived under homogeneous condition and heterogeneous condition, respectively. Furthermore, these obtained estimators are the ridge-type estimators and mean dispersion error (MDE) superior to the best linear unbiased estimator b=(X^′W^-1X)^-1X^′W^-1y$b=(X^{\prime }{W}^{-1}X{)}^{-1}{X}^{\prime }{W}^{-1}y$ under some conditions.     

A ‘nondecimated’ lifting transform

Classical nondecimated wavelet transforms are attractive for many applications. When the data comes from complex or irregular designs, the use of second generation wavelets in nonparametric regression has proved superior to that of classical wavelets. However, the construction of a nondecimated second generation wavelet transform is not obvious. In this paper we propose a new ‘nondecimated’ lifting transform, based on the lifting algorithm which removes one coefficient at a time, and explore its behavior. Our approach also allows for embedding adaptivity in the transform, i.e. wavelet functions can be constructed such that their smoothness adjusts to the local properties of the signal. We address the problem of nonparametric regression and propose an (averaged) estimator obtained by using our nondecimated lifting technique teamed with empirical Bayes shrinkage. Simulations show that our proposed method has higher performance than competing techniques able to work on irregular data. Our construction also opens avenues for generating a ‘best’ representation, which we shall explore.     

Consistency of minimizing a penalized density power divergence estimator for mixing distribution

In this paper, we study the MDPDE (minimizing a density power divergence estimator), proposed by Basu et al. (Biometrika 85:549–559, 1998), for mixing distributions whose component densities are members of some known parametric family. As with the ordinary MDPDE, we also consider a penalized version of the estimator, and show that they are consistent in the sense of weak convergence. A simulation result is provided to illustrate the robustness. Finally, we apply the penalized method to analyzing the red blood cell SLC data presented in Roeder (J Am Stat Assoc 89:487–495, 1994). This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.     

A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Using Bayesian graphical models to model biases in observational studies and to combine multiple sources of data: application to low birth weight and water disinfection by-products

Summary.  Data in the social, behavioural and health sciences frequently come from observational studies instead of controlled experiments. In addition to random errors, observational data typically contain additional sources of uncertainty such as missing values, unmeasured confounders and selection biases. Also, the research question is often different from that which a particular source of data was designed to answer, and so not all relevant variables are measured. As a result, multiple sources of data are often necessary to identify the biases and to inform about different aspects of the research question. Bayesian graphical models provide a coherent way to connect a series of local submodels, based on different data sets, into a global unified analysis. We present a unified modelling framework that will account for multiple biases simultaneously and give more accurate parameter estimates than standard approaches. We illustrate our approach by analysing data from a study of water disinfection by-products and adverse birth outcomes in the UK.     

基于多变量动态模型的产出缺口估算

 本文运用多变量动态模型系统下的Beveridge-Nelson分解方法和贝叶斯Gibbs抽样估计,估算了1985年1季度至2008年2季度期间中国的产出缺口,并且与传统的单变量估计方法测算的结果在统计属性和对货币政策调节的预测效果方面进行了比较。实证结果表明,不同产出缺口的统计属性存在差别,并且只有基于多变量系统测算的产出缺口对货币政策具有显著预测效果。这说明多变量模型估计出的产出缺口更全面地考虑了经济产出与其他相关变量的互动效应,含有的信息更为丰富,从而对宏观政策调整具有更重要的参考价值。     

浙江区域金融结构对产业集聚的影响研究 ——基于面板数据的实证分析

 以民营企业为基础的产业集聚群是浙江经济快速发展的重要原因。然而产业集聚的形成依赖于一定的外部环境,特别是对于资金的需求和金融结构有特殊的要求。本文通过对浙江11个市2000-2007年的面板数据,分析不同的金融结构对产业集聚的影响。并根据研究结论,提出了优化区域金融结构,促进浙江产业集聚群健康发展的对策建议。     

循环经济背景下企业投资的贴现因子的研究

文章基于传统耐心模型框架,针对企业投资行为带来的环境污染的影响,对相关参与人——政府和企业的耐心进行了分析,分别得出了政府和企业一次和多次博弈的收益贴现,并对政府和企业的收益贴现因子的影响因素进行了分析,为投资行为造成的环境污染治理提出了一些可供参考的解决的方法。     

“轴心期”形成的犹太教文化传统对后世之影响——兼对“犹太模式”的历史考察与未来展望

在德国哲学家雅斯贝斯提出的世界历史的"轴心期"的概念里,犹太人所创立的以犹太教为主旨内容的希伯来文明和中华文明、印度文明一样成为东西方文化传统的源头;探讨轴心期产生的犹太教对后世的基督教和伊斯兰教的影响,可以看出三者同属犹太系宗教的范畴;根据汤因比提出的三种文明解体的模式分析当今世界的格局,可以发现美国似乎正在成为罗马帝国的翻版,而道德至上的中华文明的复兴则给世界的美好未来带来了一丝希望之光。同时,由于犹太教、基督教和伊斯兰教同属犹太系宗教,有着很多根本的相同点,所以在人类要共同面对生存危机的条件下也许可以实现和解而和平共处。     

现代教育技术环境下英语教学模式探索

本文着眼于现代教育技术探究小学英语教学的新模式。