Comparison of designs equivalent under one or two criteria

Two designs equivalent under one or two criteria may be compared under other criteria. For certain configurations of eigenvalues of the information matrices, we decide which design is the better of the two for many other such criteria. The relationship to universal optimality (in the case of equivalence under one criterion) is indicated. For two criteria, applications are given to weighing and treatment-with-covariate settings.     

The construction of multi-factor crossover designs in animal husbandry studies

For ethical reasons it is important to try to obtain as much useful information as possible from an animal experiment whilst minimizing the number of animals used. Crossover designs, where applicable, provide an ideal framework for achieving this. If two or more treatment factors are included in the crossover design then the reduction in total animal usage can be considerable. In this paper we consider such designs, defined as multi-factor crossover designs. The designs are applicable when there are several different treatment factors, each at t levels, to be applied to the experimental units. The motivation for investigating these designs was a study conducted at GlaxoSmithKline to determine the preference of male and female dogs for t=5 different types of bed and t=5 different bedding conditions. A construction method is given for forming universally optimal designs for t not too large. Also given is an example for the special case where the number of treatment levels t=6.     

A plug-in the number of knots selector for polynomial spline regression

A plug-in the number of interior knots (NIKs) selector is proposed for polynomial spline estimation in nonparametric regression. The existence and properties of the optimal NIKs for spline regression are established by minimising the weighted mean integrated squared error. We obtain plug-in formulae for the optimal NIKs based on the theoretical results of asymptotic optimality, and develop strategies for choosing the NIKs of the spline estimator. The proposed NIKs selection method is tested on our simulated data with quite satisfactory performance, and is illustrated by analysing a fossil data set.     

我国农村金融市场效率内涵研究

以提高农村金融市场效率的农村金融改革不可回避的一个问题就是:如何全面认识农村金融市场效率。文章结合西方理论界对市场效率、金融市场效率的研究及我国学者的研究,提出了我国金融市场效率的内涵及评价角度。     

Benson有效点的二次必要性条件

该文引进了新的集值映射的二次切上导数概念，并利用这个概念给出了Benson有效点对必要条件．     

An inclusion-consistent solution to the problem of absurd confidence statements: 1. Consistent exact confidence-interval estimation

An example is given of a uniformly most accurate unbiased confidence belt which yields absurd confidence statements with 100% occurrence. In several known examples, as well as in the 100%-occurrence counterexample, an optimal confidence belt provides absurd statements because it is inclusion-inconsistent with either a null or an all-inclusive belt or both. It is concluded that confidence-theory optimality criteria alone are inadequate for practice, and that a consistency criterion is required. An approach based upon inclusion consistency of belts [C(x) C C C(x), for some x, implies γ ≤ γ for confidence coefficients] is suggested for exact interval estimation in continuous parametric models. Belt inclusion consistency, the existence of a proper-pivotal vector [a pivotal vector T(X, θ) such that the effective range of T(x,.) is independent of x], and the existence of a confidence distribution are proven mutually equivalent. This consistent approach being restrictive, it is shown, using Neyman's anomalous 1954 example, how to determine whether any given parametric function can be estimated consistently and exactly or whether a consistent nonexact solution must be attempted.     

Optimal design for the proportional odds model

The authors construct locally optimal designs for the proportional odds model for ordinal data. While they investigate the standard D‐optimal design, they also investigate optimality criteria for the simultaneous estimation of multiple quantiles, namely D_A ‐optimality and the omnibus criterion. The design of experiments for the simultaneous estimation of multiple quantiles is important in both toxic and effective dose studies in medicine. As with c‐optimality in the binary response problem, the authors find that there are distinct phase changes when exploring extreme quantiles that require additional design points. The authors also investigate relative efficiencies of the criteria.     

FAIR DIVISION OF INDIVISIBLE ITEMS

This paper analyzes criteria of fair division of a set of indivisible items among people whose revealed preferences are limited to rankings of the items and for whom no side payments are allowed. The criteria include refinements of Pareto optimality and envy-freeness as well as dominance-freeness, evenness of shares, and two criteria based on equally-spaced surrogate utilities, referred to as maxsum and equimax. Maxsum maximizes a measure of aggregate utility or welfare, whereas equimax lexicographically maximizes persons' utilities from smallest to largest. The paper analyzes conflicts among the criteria along with possibilities and pitfalls of achieving fair division in a variety of circumstances.     

On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

We show by example that empirical likelihood and other commonly used tests for moment restrictions are unable to control the (exponential) rate at which the probability of a Type I error tends to zero unless the possible distributions for the observed data are restricted appropriately. From this, it follows that for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications are required. Under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which the probability of a Type II error tends to zero for most alternatives. This result further implies that empirical likelihood maximizes the rate at which the probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities.     

基于阶段划分的企业主动碳减排创新策略实施研究

基于环境策略在被动阶段和主动阶段的不同,且一些企业已启动主动减排阶段的产品创新策略。本文在碳减排阶段划分的基础上,对企业主动碳减排创新策略实施进行研究,引入碳排放交易制度及政府补贴激励,构建了政策驱动下的企业主动碳减排成本收益模型和行业成本收益模型。以矩阵正定性判定企业碳减排是否存在最优策略,同时探讨该最优策略能否实现行业帕累托最优以及如何实现。研究表明,企业主动碳减排创新策略存在最优,企业对碳减排策略的投入随着其相应减排效果系数、减排收益系数与碳排放交易下政府超额补贴系数的增加而加大;行业实现帕累托最优需要政府激励政策引导,且碳排放交易下政府超额补贴系数为行业内定值,随行业内各企业减排效果与创新收益的增加而减少。此外,根据实地调研和相关文献的数据,对模型中的各项参数进行赋值,并以水泥企业为例,通过典型算例分析和关键参数灵敏度分析进行模型有效性验证。算例分析结果证实了创新收益和政府碳排放交易下的补贴激励是企业主动碳减排的关键因素。本文从阶段划分的视角对碳减排问题进行尝试性研究,可为企业主动碳减排创新策略的实施提供决策依据,同时也为政府政策制定提供参考。此外在政府引导企业碳减排帕累托改进过程中,应保障企业碳减排效率在同一水平,创新力较强的企业,减排量相应较大,从而实现碳减排的帕累托最优。