Bootstrap方法在导弹落点密集度评估中的误用

以导弹落点密集度评估作为研究基础,对利用Bootstrap方法提升小子样下落点密集度估计精度问题的自助法进行分析。在简要描述Bootstrap方法数学思想和应用方法的基础上,从理论分析和仿真验证两个方面证实了参数Bootstrap方法生成的自助统计量围绕经典估计值呈现正态分布,对于经典估计结果没有精度的提高;并且推导了自助统计量分布与估计偏差分布之间的关系,指出在小子样条件下参数Bootstrap方法自助统计量在分布近似上存在偏差;最后本文论证了随机加权法应用于密集度估计同样不能取得明显的改进效果。     

基于CVaR衍生的多期多面风险度量下的投资组合研究

为了解决多期投资组合的决策问题,本文将由CVaR衍生的多期多面风险度量作为风险控制目标,建立了一个在收益约束条件下最小化风险的多阶段投资组合模型。为求解模型,设计了多期投资组合优化流程,它将非参数抽样方法、基于聚类算法的多阶段情景树生成方法和多期多面风险度量组合在一起。该流程基于计算、容易实现、直观合理。根据我国金融市场数据进行的实证研究结果表明,这一流程具有较好的实用性。     

湿地土壤硝化微生物群落的高光谱研究

氮循环是土壤生态系统元素循环的重要过程,其中硝化作用对于土壤氮循环有重要影响。硝化作用的主要完成者是硝化微生物群落,土壤微生物是湿地生态系统的重要组成部分,其可以指示湿地生态环境变化,对正确认识湿地生态系统氮循环和湿地污染净化功能具有重要意义。尝试从高光谱遥感技术角度,基于土壤氮素光谱监测机理,探索湿地土壤硝化微生物群落高光谱估算技术,进而为估测其时空分布状况提供新技术途径。研究对硝化作用中两个独立阶段的主要完成者氨氧化细菌和亚硝酸氧化细菌,采用最大可能数法分别计数,并以两者计数测量结果的合计,作为各采样区域土壤硝化微生物的数量值。采用光谱倒数的对数(LR)、光谱一阶微分(FD)、光谱二阶微分(SD)、包络线去除(CR)和光谱波段深度(BD)光谱变换技术,以及基于再抽样(bootstrap)技术的多元逐步回归(SMLR)和偏最小二乘回归(PLSR)建模方法,构建湿地土壤硝化微生物数量和全氮含量估算模型。研究结果表明：在采用bootstrap SMLR建模方法时,湿地土壤硝化微生物数量和全氮含量的估算波段位置存在一定的相似性(尤其对于原光谱实测数据R和SD光谱);对于湿地土壤硝化微生物数量和全氮含量的估算,bootstrap PLSR相比于bootstrap SMLR建模方法,具有较高的估算精度;对湿地土壤硝化微生物数量的估算,最高估算精度产生于SD光谱变换技术结合bootstrap PLSR建模;对湿地土壤全氮含量的估算,最高估算精度产生于CR光谱变换技术结合bootstrap PLSR建模。     

进口铁矿砷量特征的内核密度分析与Bootstrap代表值估计

对进口铁矿中的砷量进行了总体统计分析, 在数据统计分布特征研究基础上, 使用内核密度估计对进口铁矿砷量进行数据多态性分析, 使用bootstrap对原始数据样本值重复取样以获得稳健的砷量代表值估计及标准偏差, 证明以bootstrap重新取样样本分布的均值与标准偏差作为有限单次样本代表值是合理、有效的.     

CVaR、VaR应用在RAROC的比较研究

本文将CVaR引入到RAROC(R isk-Ad justed Return on Cap ital)中,进行绩效评价。而且,将CVaR与VaR的结果进行了比较。在正态分布的情况下,CVaR与VaR的RAPM(R isk-Ad justedPerform ance M easure)对于绩效评价都是充分的、可靠的、有效的,且两者是等价的。但在非正态的情况下,CVaR的RAPM相对于VaR的RAPM更加充分、谨慎、可靠、有效。我们运用Bootstrap方法进行了实证研究。     

连续型经验过程及其Bootstrap逼近

本文利用样条函数将经验分布函数光滑化,从而得到了连续型经验分布函数,进而引进了连续型经验过程,本文讨论了连续型经验分布函数和连续型经验过程的渐进分布,并且证明了连续型经验过程的Bootstrap逼近成立。     

Strong law for the bootstrap

Let X₁, X₂, X₃, … be i.i.d. r.v. with E|X₁| < ∞, E X₁ = μ. Given a realization X = (X₁,X₂,…) and integers n and m, construct Y_n,i, i = 1, 2, …, m as i.i.d. r.v. with conditional distribution $\text{P}{}^1\text{(Y}{}_{\mathrm{n,i}}\text{= X}{}_{\mathrm{j}}\text{) =}\text{1}\text{n}$ for 1 ? j ? n. ($\text{P}{}^1$ denotes conditional distribution given X). Conditions relating the growth rate of m with n and the moments of X₁ are given to ensure the almost sure convergence of $\text{(}\text{1}\text{m}\text{)Σ}{}^{\mathrm{m}}{}_{\mathrm{i=1}}\text{Y}{}_{\mathrm{n,i}}$ toμ. This equation is of some relevance in the theory of Bootstrap as developed by Efron (1979) and Bickel and Freedman (1981).     

A Dirichlet process functional approach to heteroscedastic-consistent covariance estimation

The mixture of Dirichlet process (MDP) defines a flexible prior distribution on the space of probability measures. This study shows that ordinary least-squares (OLS) estimator, as a functional of the MDP posterior distribution, has posterior mean given by weighted least-squares (WLS), and has posterior covariance matrix given by the (weighted) heteroscedastic-consistent sandwich estimator. This is according to a pairs bootstrap distribution approximation of the posterior, using a Pólya urn scheme. Also, when the MDP prior baseline distribution is specified as a product of independent probability measures, this WLS solution provides a new type of generalized ridge regression estimator. Such an estimator can handle multicollinear or singular design matrices even when the number of covariates exceeds the sample size, and can shrink the coefficient estimates of irrelevant covariates towards zero, which makes it useful for nonlinear regressions via basis expansions. Also, this MDP/OLS functional methodology can be extended to methods for analyzing the sensitivity of the heteroscedasticity-consistent causal effect size over a range of hidden biases, due to missing covariates omitted from the regression; and more generally, can be extended to a Vibration of Effects analysis. The methodology is illustrated through the analysis of simulated and real data sets. Overall, this study establishes new connections between Dirichlet process functional inference, the bootstrap, consistent sandwich covariance estimation, ridge shrinkage regression, WLS, and sensitivity analysis, to provide regression methodology useful for inferences of the mean dependent response.     

Recent Advances in the Catalytic Synthesis of the Cyclopentene Core

Five-membered carbocycles are ubiquitously found in natural products, pharmaceuticals, and other classes of organic compounds. Within this category, cyclopentenes deserve special attention due to their prevalence as targets and as well as key intermediates for synthesizing more complex molecules. Herein, we offer an overview summarizing some significant recent advances in the catalytic assembly of this structural motif. A great variety of synthetic methodologies and strategies are covered, including transition metal-catalyzed or organocatalyzed processes. Both inter- and intramolecular transformations are documented. On this ground, our expertise in the application of C−H functionalization reactions oriented towards the formation of this ring and its subsequent selective functionalization is embedded.