On biased linear estimators in models with arbitrary rank

In this paper we define a class of biased linear estimators for the unknown parameters in linear models with arbitrary rank. The feature of our approach is to reduce the estimation problem in arbitrary rank models to the one in full-rank models. Some important properties are discussed. As special cases of our class, we extend to deficient-rank models six known biased linear estimators.     

A study of ratio and product estimators under a super population model

In this paper ratio and product estimators are studied under a super population model considered by Durbin (1959. Biometrika) where a regression model of y (the characteristic variablel on x(the auxiliary variable) is assumed. The comparison of the ratio and the product estimators have been made in the literature (see Chaubey, Dwivedi and Singh (1984), Commun. Statist. - Theor. Meth.) When the auxiliary variable has a gamma distribution. In this paper similar analysis has been carried out when the auxiliary variable has an inverse Gaussian distribution.     

A note on the semiparametric approach to dimension reduction

Abstract

In this note, we present a theoretical result which relaxes a critical condition required by the semiparametric approach to dimension reduction. The asymptotic normality of the estimators still maintains under weaker assumptions. This improvement greatly increases the applicability of the semiparametric approach.     

The Inverse Relation Between Risks and Benefits: The Role of Affect and Expertise

Although risk and benefits of risky activities are positively correlated in the real world, empirical results indicate that people perceive them as negatively correlated. The common explanation is that confounding benefits and losses stems from affect. In this article, we address the issue that has not been clearly established in studies on the affect heuristic: to what extent boundary conditions, such as judgments’ generality and expertise, influence the presence of the inverse relation in judgments of hazards. These conditions were examined in four studies in which respondents evaluated general or specific benefits and risks of “affect‐rich” and “affect‐poor” hazards (ranging from investments to applications of stem cell research). In line with previous research, affect is defined as good or bad feelings integral to a stimulus. In contrast to previous research, affect is considered as related both to personal feelings and to social controversies associated with a hazard. Expertise is related to personal knowledge (laypersons vs. experts) as well as to objective knowledge (targets well vs. poorly known to science). The direct comparison of the input from personal and objective ignorance into the inverse relation has not been investigated previously. It was found that affect invoked by a hazard guides general but not specific judgments of its benefits and risks. Technical expertise helps to avoid simplified evaluations of consequences as long as they are well known to science. For new, poorly understood hazards (e.g., stem cell research), expertise does not protect from the perception of the inverse relation between benefits and risks.     

Expected and unexpected values of individual Mahalanobis distances

This paper derives first-order sampling moments of individual Mahalanobis distances (MDs) in cases when the dimension p of the variable is proportional to the sample size n. Asymptotic expected values when n, p → ∞ are derived under the assumption p/n → c,?0 ? c < 1. It is shown that some types of standard estimators remain unbiased in this case, while others are asymptotically biased, a property that appears to be unnoticed in the literature. Second-order moments are also supplied to give some additional insight to the matter.     

基于计算—实验综合模型的啮合齿面关键摩擦特性参数反求研究

在齿轮传动动测实验的基础上,引入有限单元法多场耦合分析和反求技术,提出了面向工程的复杂齿轮传动摩擦多性态概念,建立了复杂齿轮传动的"计算—实验综合模型";利用该综合模型对不同润滑状况下齿面摩擦因数进行了合理的反求,解决了复杂曲面摩擦因数难于求解的问题。     

基于copula回归模型的损失预测

在非寿险损失预测的广义线性模型中,通常假设损失次数与损失强度相互独立,事实上二者之间往往存在一定的相依关系,可通过copula函数来刻画.在损失已经发生的条件下,假设损失次数服从零截断泊松分布,损失强度服从伽玛分布,可以建立损失次数与损失强度相互依赖的copula回归模型.把损失强度的分布扩展到逆高斯分布,并将此模型应用于一组车险保单数据进行实证研究.结果表明:该模型不但在损失预测方面优于独立假设下的广义线性模型,而且也优于损失强度服从伽马分布假设下的copula回归模型.     

Bayesian Recovery of the Initial Condition for the Heat Equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying “smoothness” and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case, credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.     

回头背书制度的完善建议

承认回头背书是票据作为流通证券的当然结果,无须也不应根据《票据法》第69条规定解释。承认回头背书与承认回头背书的被背书人的再背书权是不同的两个问题。《票据法》并没有承认回头背书被背书人的再背书权。为促进票据流通,《票据法》有必要明确这一例外,修订因回头背书导致的追索权限制问题、人的抗辩切断问题,并赋予回头背书被背书人之后手的追索权。