Frontiers of Stochastically Nondominated Portfolios

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution.We propose mean‐risk models that are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second‐order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean‐risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations.     

“最大多数人”与“最少受惠者”——两种正义观的伦理基础及其模糊性

在边沁、密尔的功利主义与罗尔斯正义论两种立场迥异的分配正义观中,两个社会群体分别成为各自伦理判断的基础,即最大多数人与最少受惠者。然而,两者都未能确定无疑地界定谁是真正的最大多数人或最少受惠者,导致两种分配伦理原则在实践中面临诸多困难。功利主义用最大多数人替代全体人,致使其界定的最大幸福含义模糊不清,据此,政府在制定公共政策时很难准确判断特定的受惠对象,最终以牺牲少数人的利益换取最大多数人的幸福。罗尔斯则将正义原则建立在最少受惠者利益基础之上,克服了功利主义最大多数人的不确定性,以收入指标确定最少受惠者地位,但对个人标准的表述却又过于具体与特殊,以至于无法给出一个清晰的标准,同样给决策者以模棱两可的信息。由于两种正义观的理论矛盾并非通过其自身的理论修正可以克服,因而需要在冲突中相互吸收与融合才能得以消解。     

Testing explosive bubbles with time-varying volatility

This article considers the problem of testing for an explosive bubble in financial data in the presence of time-varying volatility. We propose a weighted least squares-based variant of the Phillips et al.) test for explosive autoregressive behavior. We find that such an approach has appealing asymptotic power properties, with the potential to deliver substantially greater power than the established OLS-based approach for many volatility and bubble settings. Given that the OLS-based test can outperform the weighted least squares-based test for other volatility and bubble specifications, we also suggest a union of rejections procedure that succeeds in capturing the better power available from the two constituent tests for a given alternative. Our approach involves a nonparametric kernel-based volatility function estimator for computation of the weighted least squares-based statistic, together with the use of a wild bootstrap procedure applied jointly to both individual tests, delivering a powerful testing procedure that is asymptotically size-robust to a wide range of time-varying volatility specifications.     

存在退保时分红寿险定价的最小二乘蒙特卡罗模拟

分红型人寿保险保单可以视作由三部分构成:固定收益债券、分红权和退保权.退保权的存在使保单具有美式期权的性质,给定价带来困难.本文用最小二乘蒙特卡罗模拟,建立了计算保单价值的模型,给出了模拟计算结果.     

具有特殊性质的保凸样条及算法

给出一种具有特殊性质的保凸插值样条及算法 ,这无论是对有关问题的理论研究 ,还是实际应用都具有一定的意义     

椭圆边值问题的Galerkin法及最小二乘法处理

讨论了椭圆边值问题的Galerkin法,并对导数作出最小二乘法处理,从而得到超收敛结果.     

Robust extrapolation designs and weights for biased regression models with heteroscedastic errors

We consider the construction of designs for the extrapolation of regression responses, allowing both for possible heteroscedasticity in the errors and for imprecision in the specification of the response function. We find minimax designs and correspondingly optimal estimation weights in the context of the following problems: (1) for ordinary least squares estimation, determine a design to minimize the maximum value of the integrated mean squared prediction error (IMSPE), with the maximum being evaluated over both types of departure; (2) for weighted least squares estimation, determine both weights and a design to minimize the maximum IMSPE; (3) choose weights and design points to minimize the maximum IMSPE, subject to a side condition of unbiasedness. Solutions to (1) and (2) are given for multiple linear regression with no interactions, a spherical design space and an annular extrapolation space. For (3) the solution is given in complete generality; as one example we consider polynomial regression. Applications to a dose-response problem for bioassays are discussed. Numerical comparisons, including a simulation study, indicate that, as well as being easily implemented, the designs and weights for (3) perform as well as those for (1) and (2) and outperform some common competitors for moderate but undetectable amounts of model bias.     

生长曲线最小二乘估计和最佳线性无偏估计相等的几个充要条件

讨论了生长曲线未知参数的最小二乘估计与最佳线性无偏估计相等的几个充要条件,并给出了主要结论的两种不同证明。     

A semiparametric pseudo-score method for analysis of two-phase studies with continuous phase-I covariates

Two-phase study designs can reduce cost and other practical burdens associated with large scale epidemiologic studies by limiting ascertainment of expensive covariates to a smaller but informative sub-sample (phase-II) of the main study (phase-I). During the analysis of such studies, however, subjects who are selected at phase-I but not at phase-II, remain informative as they may have partial covariate information. A variety of semi-parametric methods now exist for incorporating such data from phase-I subjects when the covariate information can be summarized into a finite number of strata. In this article, we consider extending the pseudo-score approach proposed by Chatterjee et al. (J Am Stat Assoc 98:158–168, 2003) using a kernel smoothing approach to incorporate information on continuous phase-I covariates. Practical issues and algorithms for implementing the methods using existing software are discussed. A sandwich-type variance estimator based on the influence function representation of the pseudo-score function is proposed. Finite sample performance of the methods are studies using simulated data. Advantage of the proposed smoothing approach over alternative methods that use discretized phase-I covariate information is illustrated using two-phase data simulated within the National Wilms Tumor Study (NWTS).     

多波长最小二乘回归-分光光度法同时测定环境水中的NO3-和NO2-离子

本文研究了利用多波长最小二乘回归-分光光度法同时测定环境水中的NO3-和NO2-离子含量的方法.通过选择合适的测试条件,利用多波长最小二乘回归计算水中NO3-和NO2-离子的含量,并与最大吸收峰值法进行比较,结果表明,多波长最小二乘回归法优于后者.