A fresh approach for intercession of nonresponse in multivariate longitudinal designs

The occurrence of nonresponse is very much plebeian in surveys, which troubles the analysis, and hence, an inappropriate inference is left out. To counterbalance the sour effects of the incompleteness, fresh imputation techniques have been proposed with the aid of multi-auxiliary variates for the estimation of population mean on successive waves. Properties of the proposed estimators have been elaborated, and they have been compared with the work of Priyanka et al. (2015). Detailed simulation study is carried out to substantiate the empirical and theoretical results. Several possible cases have been addressed in which nonresponse can occur.     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.     

最优货币理论与中国货币统一

最优货币区理论为欧洲货币联盟提供了理论依据,欧元的流通对世界经济产生了深远影响。主要针对亚洲地区建立统一货币的困境,提出统一中国货币以及构建大中华经济圈的设想。     

积分变换求梁的变形

本文从求解梁挠度的二阶差分方程出发,通过Z变换,最后推导出计算挠度和转角的简单公式,使计算过程简化。对于变截面梁和复杂受载下,此法尤为简便。同时,这也是处理离散参数的数学方法—Z变换在力学中应用的初步尝试。     

中国和东盟国家的最优货币区指数分析

按照蒙代尔等提出的建立最优货币区的标准,影响建立货币联盟的因素很多,而每一个标准都只是从某一个方面分析建立货币联盟应达到的条件,没有将各个因素综合起来,从总体上分析一个地区是否应建立货币联盟,或者一个国家是否应该加入货币联盟。最优货币区(OCA)指数将汇率波动和反映最优货币区标准的指标的波动进行回归,通过模型将这些标准结合起来,可以综合分析各个因素对中国和东盟国家建立单一货币区的影响,为建立货币联盟提供一个综合的标准,并且可以分析各国在建立货币联盟时,可供选择的锚货币和建立货币联盟的步骤。     

Confidence intervals for extreme Pareto-type quantiles

In this paper, we revisit the construction of confidence intervals for extreme quantiles of Pareto-type distributions. A novel asymptotic pivotal quantity is proposed for these quantile estimators, which leads to new asymptotic confidence intervals that exhibit more accurate coverage probability. This pivotal quantity also allows for the construction of a saddle-point approximation, from which a second set of new confidence intervals follows. The small-sample properties and utility of these confidence intervals are studied using simulations and a case study from insurance.     

新建高校筹资最优资本结构的方案分析

分析近年来我国新建高校筹资建设的实际情况,提出确立最优筹资方案,为学校多渠道筹措资金、化解风险、保证高校建设拓宽思路。     

Optimal and Acceptable Technical Facilities Involving Risks

Economic cost-benefit optimization of technical facility requires suitable "life saving cost" and/or an appropriate acceptance criterion if human life and limb are at risk. Traditionally, acceptance criteria implicit in codes of practice, standards, or regulations for well-defined fields of application are calibrated against past and present practice. This is all but satisfying. It is unclear whether present rules are already optimal. Extrapolations into new fields of application are extremely difficult. Direct cost-benefit analysis is proposed as an alternative. Based on the recently proposed "life quality index" (LQI), a rational acceptance criterion and so-called life saving cost are derived. The classical life quality index is reviewed, modified, and imbedded in modern economics theory. The results are then applied to technical facilities. The relation between optimization and the LQI-based acceptance criterion is discussed. The relevant economics literature is reviewed with respect to discount rates applicable for long-term investments into risk reduction. They should be as low as possible according to a recent mathematical result. Modern economic growth theory decomposes the output growth rate into the rate of time preference of consumption and the rate of economical growth multiplied by the elasticity of marginal utility of consumption. It is found that the rate of time preference of consumption should be a little larger than the long-term population growth rate. The public benefit rate (output growth rate) on the other hand should be smaller than the sum of the population growth rate and the long-term growth rate of a national economy, which is around 2% for most industrial countries. Accordingly, the rate of time preference of consumption is about 1%, which is also intergenerationally acceptable from an ethical point of view. Given a certain output growth rate there is a corresponding maximum financial interest rate in order to maintain nonnegativity of the objective function at the optimum. Finally, a simple demonstration example is added.     

Convexity-based clustering criteria: theory,algorithms, and applications in statistics

This paper deals with the construction of optimum partitions of for a clustering criterion which is based on a convex function of the class centroids as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs -divergence) and for simultaneous classification of the rows and columns of a contingency table.     

Sequential experimental design and response optimisation

We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy _k . This may correspond to the case of a regression model, where one observesy _k =f(θ,x _k )+ε _k , with ε _k some random error, or to the Bernoulli case wherey _k ∈{0, 1}, with Pr[y _k =1|θ,x _k |=f(θ,x _k ). Special attention is given to sequences given by , with an estimated value of θ obtained from (x₁, y₁),...,(x _k ,y _k ) andd _k (x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon, where one wants to maximize ∑ _i=1 ^N w _i f(θ, x _i ) with {w _i } a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method for a binary response problem.