Powerful Trend Function Tests That Are Robust to Strong Serial Correlation,With an Application to the Prebisch–Singer Hypothesis

We propose tests for hypotheses on the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data, and they are robust to strong serial correlation. The data can contain a unit root and still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze these tests using the fixed-b asymptotic framework recently proposed by Kiefer and Vogelsang. This analysis allows us to analyze the power properties of the tests with regard to bandwidth and kernel choices. Our analysis shows that among popular kernels, specific kernel and bandwidth choices deliver tests with maximal power within a specific class of tests. Based on the theoretical results, we propose a data-dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang. We apply the recommended test to the logarithm of a net barter terms of trade series and we find that this series has a statistically significant negative slope. This finding is consistent with the well-known Prebisch–Singer hypothesis.     

On distribution function estimation with partially rank-ordered set samples: estimating mercury level in fish using length frequency data

We study the non-parametric estimation of a continuous distribution function F based on the partially rank-ordered set (PROS) sampling design. A PROS sampling design first selects a random sample from the underlying population and uses judgement ranking to rank them into partially ordered sets, without measuring the variable of interest. The final measurements are then obtained from one of the partially ordered sets. Considering an imperfect PROS sampling procedure, we first develop the empirical distribution function (EDF) estimator of F and study its theoretical properties. Then, we consider the problem of estimating F, where the underlying distribution is assumed to be symmetric. We also find a unique admissible estimator of F within the class of nondecreasing step functions with jumps at observed values and show the inadmissibility of the EDF. In addition, we introduce a smooth estimator of F and discuss its theoretical properties. Finally, we expand on various numerical illustrations of our results via several simulation studies and a real data application and show the advantages of PROS estimates over their counterparts under the simple random and ranked set sampling designs.     

Partitioned cross-validation

Partitioned cross-validation is proposed as a method for overcoming the large amounts of across sample variability to which ordinary cross-validation is subject. The price for cutting down on the sample noise is that a type of bias is intriduced. A theory is presented for optimal trade-off of this variance and bias. Comparison with other bandwidth selection methods is given.     

一种评价信息不完全的混合型多属性群决策方法

针对一类评价信息不完全且属性值由精确数、语言评价值等定量、定性形式构成的混合型不完全信息多属性群决策问题,提出了一种基于直觉模糊集和证据理论的决策方法。首先定义了转换函数将不同类型属性值一致转换为更符合决策实际的直觉模糊数,接着根据信息熵原理利用直觉模糊数中的犹豫度确定专家客观权重,随后应用证据理论集结含有信息缺失的评价值,并构造了一可能度比较公式用于集结后方案排序。该法解决了决策问题中易出现的信息残缺和混合型信息等情况,具有更强的实用性。最后的实例分析证明了该方法的科学性、有效性。     

基于熵权法的人的全面发展评价模型及“十五”期间的实证

根据"坚持以人为本,全面、协调、可持续的发展观",基于经济发展环境、社会发展环境、生态环境、人力资本环境、生活质量和人口素质评价准则,利用客观赋权的熵权法对指标进行赋权,建立了基于熵权法的人的全面发展综合评价模型,并对中国"十五"期间人的全面发展情况进行评价,提出了相应的政策建议.特色与创新体现在:①根据人与自然和谐、人与社会和谐、人与人和谐的原则建立指标体系,使对人的全面发展的评价反映科学发展观的要求,克服了现有指标体系及其选取规则不合理的问题;②通过熵权法赋权反映了客观数据所体现的指标间的差异,且在对未来数据的推断中反映客观权重的变化,避免了主观赋权法存在人为分配权重不合理的现象;③通过对中国"十五"期间人的全面发展的综合评价中发现的问题,给出了中国"十一五"期间乃至更长时间内人的全面发展的针对性政策建议,建立了评价结果与改进措施的有机联系,有利于评价对象的自我管理和完善.     

组合评价方法在银行信用风险评价中的应用

针对贷款客户评价选择问题,在对已有研究方法分析的基础上,提出了以熵权与偏好顺序结构评估法相结合的排序方法。以借贷人的财务状况、借贷人的管理水平、借贷人的行业地位、借贷人资产的变现性和借贷人历史信用状况为评价准则,利用信息熵来确定评价准则的权重,用偏好顺序评价法确定贷款客户的贷款顺序,并进行了灵敏度分析。最后通过算例证明了该方法的有效性。     

我国区域科技发展不均衡及其成因研究

从熵理论出发,引入THEIL不均衡指数,对我国区域科技发展水平的不均衡性进行了定量评价,结果显示:在20世纪90年代初,我国各地区科技发展水平的不均衡性有较大的改善,但从1993年开始,不均衡性又逐渐增加。针对这一现实问题,对我国区域科技发展不均衡特征与趋势及其成因进行了相关探讨。     

从生态学的层面以能量流动解析社会发展过程

为了更好地理解社会发展的本质，进一步构建和谐社会，从生态学的层面解析了社会发展过程。论述了发展的本质是能量的流动、追求有序，发展的方向是负熵能量流动的方向。人产生于自然发展过程之中，人本身是自然最伟大的创造，需要最大的负熵能量流动，这样，自然相对于人具有先在性。科学发展观的以人为本体现了现实的人、人类思维、人的创造性等有关人的逻辑，从而揭示人是社会发展的本质。分析了社会保障、劳动就业、教育与人的发展的关系，及广泛联系的生态关系延伸进入社会，如何构筑了社会和谐发展的逻辑。指出：在科学发展观指导下的和谐社会的构建，就是要建设中国特色的社会主义和谐社会。     

基于相对熵方法的长寿债券定价研究

本文在风险中性测度理论的框架下对经典的长寿风险衍生品——EIB/BNP型长寿债券进行了定价。文章首先使用Cairns-Blake-Dowd两因子模型，模拟预测了我国高龄人口未来的死亡率路径，然后通过引入三种相对熵，即Kullback-Leibler相对熵、Tsallis相对熵以及Rényi相对熵，并依据最小相对熵准则确定最优风险中性测度，进而完成对长寿债券的定价。在定价的过程中，本文融入已在我国市场发行的不同期限金融债的风险溢价信息，使定价结果更合理地反映我国金融市场规律。从计算方法上看，不同相对熵模型的定价保证了计算结果的稳健性和可信性；本文还发现对冲女性长寿风险所需的溢价整体上要高于对冲男性长寿风险所需的溢价，表明女性长寿风险面临的不确定性程度更大。本文还分别比较了仅融合单一市场风险价格以及考虑多个市场风险价格作为先验信息时定价结果的差异，发现定价的结果对市场信息依赖程度较高。这也表明了相对熵方法的可塑性较强，随着市场完全度的提高和我国金融市场的发展，该方法的定价结果将更趋于合理。文章最后一部分是总结和启示。     

Maximum Entropy Approximations for Asymptotic Distributions of Smooth Functions of Sample Means

Abstract. We propose an information‐theoretic approach to approximate asymptotic distributions of statistics using the maximum entropy (ME) densities. Conventional ME densities are typically defined on a bounded support. For distributions defined on unbounded supports, we use an asymptotically negligible dampening function for the ME approximation such that it is well defined on the real line. We establish order n^?1 asymptotic equivalence between the proposed method and the classical Edgeworth approximation for general statistics that are smooth functions of sample means. Numerical examples are provided to demonstrate the efficacy of the proposed method.