Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

Macroeconomic asymmetry in the Eurozone before and after the Global Financial Crisis: An appraisal of the role of the ECB

The launch of the euro in 1999 was assumed to enhance macroeconomic convergence among EMU economies. We test this hypothesis from a comparative perspective, by calculating different indices to measure the degree of macroeconomic dispersion within the Eurozone, the UK and the USA (1999–2019). We use common factor models to produce a single index for each monetary area out of different measures of dispersion. These indices can be used to inform on the degree of optimality of a monetary area. Our results show that macroeconomic dispersion in the Eurozone increased notably even before 2007 and it took significantly longer to return to pre-crisis levels, as compared to the UK and the USA. The paper shows the critical role played by the ECB’s asset purchases programmes in reducing macroeconomic divergences among EMU member states since 2015.     

媒介融合概念的解析与层次

媒介融合已成为学术热点,但学界对于什么是媒介融合、媒介融合的层次划分等基本问题依然缺乏足够讨论。通过梳理国内外学界有关媒介融合的研究文献发现,虽然融合一词是这一概念的核心,但媒介融合概念的界定却在很大程度上取决于媒介一词,并且至少可以从技术、经济、组织以及制度四个维度来分析和理解其内涵和层次;同时,媒介融合不仅是一个涉及技术、经济、组织以及制度等多个构面和层次的概念,而且是人类社会发展进程中一个全新"技术-经济范式"的内核。     

中国绿色农业技术效率及其省际差异分析——基于1998—2012年的面板数据

基于1998—2012年面板数据,运用熵值法和DEA模型测算中国绿色农业产出和绿色农业技术效率,并分析其省际差异。研究表明,中国农业已经初具绿色转型的趋势,除东北地区外,其他地区绿色农业技术效率均上升;中国绿色农业技术效率有所提升,但整体水平仍然低下。东部、西部、东北、中部地区效率依次递减;全国省域间效率绝对差距没有缩小趋势,但相对差距明显缩小。东部、中部、西部和东北地区各地区内省域间绝对差距均没有缩小趋势,但东部、中部地区各地区内省域间相对差距存在缩小趋势,而西部、东北地区没有缩小趋势。全国2/3的省份绿色农业技术效率低下但处于增长态势;东北三省和内蒙古、宁夏、新疆陷入效率低下且呈下降态势的双重困境。     

网络信息产业融合机理与发展策略研究

随着网络信息技术的日益发展,信息技术产业的融合之势愈加明显,各种新兴网络应用服务层出不穷。信息产业融合型的增长模式正在快速改变着社会经济的运行方式。产业融合正在加速产业结构的变动调整,也在推动产业转型升级。产业间的融合渗透促进了新兴业务的活跃爆发,为产业发展带来了一股全新的力量。应当以此为契机,培育新一代产业增长极。首先需要认清产业发展规律,科学地指导产业发展;其次有必要打破体制壁垒,创造良好的政策支持环境;再者,营造开放的发展环境,鼓励企业创新,从而以产业融合有力地推动网络信息产业发展。     

基于产业融合的历史文化街区型商业区发展规划———以安阳市文峰特色商业区为例

以安阳文峰特色商业区为例,提出了历史文化街区型特色商业区的发展思路与理念,明确了产业发展方向与重点,从而构建了产业发展的基本路径与框架.     

对零势点选择若干问题的探讨

讨论几种典型电场的零势点位置的确定 ,说明选择零势点的原则     

Asymptotic Analysis of the Sieve Estimator for a Class of Parabolic SPDEs

In this paper we consider the problem of estimating a coefficient of a strongly elliptic partial differential operator in stochastic parabolic equations. The coefficient is a bounded function of time. We compute the maximum likelihood estimate of the function on an approximating space (sieve) using a finite number of the spatial Fourier coefficients of the solution and establish conditions that guarantee consistency and asymptotic normality of the resulting estimate as the number of the coefficients increases. The equation is assumed diagonalizable in the sense that all the operators have a common system of eigenfunctions.     

Nonparametric regression estimates with censored data based on block thresholding method

Here we consider wavelet-based identification and estimation of a censored nonparametric regression model via block thresholding methods and investigate their asymptotic convergence rates. We show that these estimators, based on block thresholding of empirical wavelet coefficients, achieve optimal convergence rates over a large range of Besov function classes, and in particular enjoy those rates without the extraneous logarithmic penalties that are usually suffered by term-by-term thresholding methods. This work is extension of results in Li et al. (2008). The performance of proposed estimator is investigated by a numerical study.     

Cross-Validated Assessments of Test Scoring Models

On a multiple choice test in which each item has r alternative options, a given number c of which are correct, various scoring models have been proposed. In one case the test-taker is allowed to choose any size solution subset and he/she is graded according to whether the subset is small and according to how many correct answers the subset contains. In a second case the test-taker is allowed to select only solution subsets of a prespecified maximum size and is graded as above. The first case is analogous to the situation where the test-taker is given a set of r options with each question; each question calls for a solution which consists of selecting that subset of the r responses which he/she believes to be correct. In the second case, when the prespecified solution subset is restricted to be of size at most one, the resulting scoring model corresponds to the usual model, referred to below as standard. The number c of correct options per item is usually known to the test-taker in this case.

Scoring models are evaluated according to how well they correctly identify the total scores of the individuals in the class of test-takers. Loss functions are constructed which penalize scoring models resulting in student scores which are not associated with the students true (or average) total score on the exam. Scoring models are compared on the basis of cross-validated assessments of the loss incurred by using each of the given models. It is shown that in many cases the assessment of the loss for scoring models which allow students the opportunity to choose more than one option for each question are smaller than the assessment of the loss for the standard scoring model.