Kiefer–Wolfowitz algorithm under quasi-associated random errors

In this article, we study the algorithm of Kiefer–Wolfowitz underquasi-associated random errors. We establish the complete convergence and obtain an exponential bound. Additionally, we build a confidence interval for the minimum. Numerical examples are sketched out to confirm the theoretical results and show the accuracy of the algorithm.     

On the Nonlinear Predictability of Stock Returns Using Financial and Economic Variables

In a recent article by Qi, neural networks trained by Bayesian regularization were used to predict excess returns on the S&P 500. The article concluded that the switching portfolio based on the recursive neural-network forecasts generates higher accumulated wealth with lower risks than that based on linear regression. Unfortunately, attempts to replicate the results were unsuccessful. Replicated results using the same software, approach and data detailed by Qi indicate that, in fact, the switching portfolio based on the recursive neural-network forecasts generates lower accumulated wealth with higher risks than that based on linear regression.     

依存距离最小化是人类语言的普遍规律吗？

麻省理工学院（ MIT ）大脑与认知科学系的弗特勒尔等人对 37 种自然语言的进行了基于语料库的大数据分析,为人类语言中的依存距离最小化倾向提供了最新的实证依据,在科学研究领域引起广泛关注。 MIT 这项研究可能是迄今为止含有语言最多的依存距离研究,在普遍性的验证上较先前研究更为全面,在方法上也有自身的一些特点。但其结论与看法有多处值得商榷。早在八年前,浙江大学刘海涛团队对依存距离最小化倾向进行了较为深入的研究,推动了人们了解人类语言如何在普遍认知机制制约下形成与演化,也帮助人们更深入地认识人类的认知机制。这些研究充分体现了语言研究是一个具有交叉学科特点的研究领域,是多语言、大数据技术、语言的普遍规律、认知科学充分融合的学科。这四大因素结合起来的研究将会展现当代科学研究的光芒,并将对当代语言科学的发展起到重要的推动作用。     

从法理上对税收负担最小化手段的再界定——税收筹划概念的内涵和外延

目前关于税收负担最小化手段的理解多种多样 ,对税收筹划及相关概念的使用很不规范 ,容易误导纳税人的行为和国家的税收征管。本文从法理上将税收负担最小化手段划分为偷逃骗税和税收筹划 ,又将税收筹划划分为避税、节税和税负转嫁     

语言学的交叉学科研究：语言普遍性、人类认知、大数据

麻省理工学院学者近期发表在国际顶尖期刊《美国科学院院报》上的一项语言学交叉研究利用已经公开发布的依存树库，对37种语言进行了统计分析，指出人类语言存在依存距离最小化这一倾向。此研究被媒体热议，但却存在一些缺陷。依存距离是两个句法相关词之间的线性距离，受工作记忆机制的约束，与句法处理的复杂度密切相关。因此，人类语言具有依存距离最小化的倾向。基于句法标注语料库的依存距离最小化研究表明，大数据研究方法在语言认知研究中具有重要作用。现代语言学具有鲜明的交叉学科色彩，语言研究中不同学科的相互借鉴与融合有助于深入揭示语言系统的运作规律以及语言与认知之间的关系。     

A Note on Importance Resampling for Multi-Dimensional Statistics

Johns (1988 Johns , M. V. (1988). Importance sampling for bootstrap confidence intervals. Journal of the American Statistical Association 83:709–714.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Davison (1988 Davison , A. C. ( 1988 ). Discussion of paper by D. V. Hinkley . Journal of the Royal Statistical Society Series B 50 : 356 – 357 . [Google Scholar]), and Do and Hall (1991 Do , K. A. , Hall , P. ( 1991 ). On importance sampling for the bootstrap . Biometrika 78 : 161 – 167 .[Crossref], [Web of Science ®] , [Google Scholar]) used importance sampling for calculating bootstrap distributions of one-dimensional statistics. Realizing that their methods can not be extended easily to multi-dimensional statistics, Fuh and Hu (2004 Fuh , C. D. , Hu , I. ( 2004 ). Efficient importance sampling for events of moderate deviations with applications . Biometrika 91 : 471 – 490 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed an exponential tilting formula for statistics of multi-dimension, which is optimal in the sense that the asymptotic variance is minimized for estimating tail probabilities of asymptotically normal statistics. For one-dimensional statistics, Hu and Su (2008 Hu , J. , Su , Z. ( 2008 ). Adaptive resampling algorithms for estimating bootstrap distributions . Journal of Statistical Planning and Inference 138 ( 6 ): 1763 – 1777 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed a multi-step variance minimization approach that can be viewed as a generalization of the two-step variance minimization approach proposed by Do and Hall (1991 Do , K. A. , Hall , P. ( 1991 ). On importance sampling for the bootstrap . Biometrika 78 : 161 – 167 .[Crossref], [Web of Science ®] , [Google Scholar]). In this article, we generalize the approach of Hu and Su (2008 Hu , J. , Su , Z. ( 2008 ). Adaptive resampling algorithms for estimating bootstrap distributions . Journal of Statistical Planning and Inference 138 ( 6 ): 1763 – 1777 .[Crossref], [Web of Science ®] , [Google Scholar]) to multi-dimensional statistics, which applies to general statistics and does not resort to asymptotics. Empirical results on a real survival data set show that the proposed algorithm provides significant computational efficiency gains.     

Minimizing the expected sample range

Let X_i be i.i.d. random variables with finite expectations, and θ_i arbitrary constants, i=1,…,n. Y_i=X_i+θ_i. The expected range of the Y's is R_n(θ₁,…,θ_n)=E(maxY_i-minY_i. It is shown that the expected range is minimized if and only if θ₁=?=θ_n. In the case where the X_i are independently and symmetrically distributed around the same constant, but not identically distributed, it is shown that θ₁=?=θ_n are not necessarily the only (θ₁,...,θ_n) minimizing R_n. Some lemmas which are applicable to more general problems of minimizing R_n are also given.     

The Pathways Model as Harm Minimization for Youth Gamblers in Educational Settings

Prevalence studies have indicated that a significant percentage of school-age youth exhibit problem or pathological gambling behaviors. However, to date there are few guidelines to assist educators in identifying those at risk and incorporating harm-reduction strategies into school curricula. This paper proposes using the Pathways Model of pathological gambling (Blaszczynski, 1998; Blaszczynski & Nower, 2002) as a harm-minimization strategy to guide social workers and other educators in effectively assessing, discriminating, and managing discrete subgroups of youth problem gamblers in educational settings and referring them to appropriate services. The Pathways Model asserts that a multiple range of specific psychological, biological, and socio-ecological variables interact at differential levels to form three distinct routes leading to the manifestation of superficially similar phenomenological characteristics and symptoms. It is argued that an understanding of the relevance and psychological implications of each separate pathway will greatly assist in the application of early intervention and prevention strategies, designed to effectively minimize the potential harm associated with youth problem gambling behaviors.     

Visualizing Mean,Median, Mean Deviation,and Standard Deviation of a Set of Numbers

We review the existing visualizations of the mean and the median of a given set of numbers. Then we give an alternative visualization of the mean using the empirical cumulative distribution function of the given numbers. Next, we visualize the mean deviation (MD) and the mean square deviation (MSD) of the given numbers from any arbitrary value, including the variance. In light of these new visualizations, we revisit the well-known optimal properties of the MD from the median and the MSD from the mean. We also give a more elementary explanation of why the denominator of the sample variance of a set of numbers is one less than the sample size.     

Intermediate Monitoring,Sample Size Reassessment,and Multi-Treatment Optimal Response-Adaptive Designs for Phase III Clinical Trials with More Than One Constraint

Optimal response-adaptive designs in Phase III clinical trial set up are becoming more and more current interest. In the present article, an optimal response-adaptive design is introduced for more than two treatments at hand. We minimize an objective function subject to more than one inequality constraints. For this purpose, we propose an extensive computer search algorithm. The proposed procedure is illustrated with extensive numerical computation and simulations. Some real data set is used to illustrate the proposed methodology.