沪深股市的风险测度研究

本文比较风险测度方法在不同置信水平下是否能力有效测度沪深市场风险.针对上证综指收益率具有自相关、波动集聚性和杠杆效应特征,运用ARMA-GJR模型对上证综指的负收益率序列进行MLE以求出条件均值和方差以及标准残差序列,运用10%的数据作为极值数据运用MLE方法来估计广义帕累托分布,还对风险测度方法的估计效果进行分析,认为极值VaR能有效测度沪深股市风险.     

Box-Cox变换下联合均值与方差模型的极大似然估计

在提出Box-Cox变换下联合均值与方差模型的基础上,研究了该模型参数的估计问题.同时利用截面极大似然估计方法对变换参数λ进行估计,并对均值模型和方差模型的参数进行极大似然估计.通过随机模拟和实例研究,结果表明该模型和方法是有效和可行的.     

不完全市场中不连续股价的动态资产分配

在不完全市场条件下,当股票价格服从跳跃扩散过程时,文章通过确定方差-最优鞅测度,讨论了动态资产分配问题,给出了动态均值-方差有效策略和有效前沿的解析表达式并且证明了均值-方差有效前沿在期望收益-标准差空间是直线.     

基于Copula的最优投资组合探讨

文章以马克维茨的投资组合理论为基础,在均值-方差模型中引入Copula理论,使用Copula函数导出的时变KendallΥ 来代替传统的线性相关系数对相关性进行测度,求解基于Υ的最优投资组合模型,得到最优投资组合对应的方差,并且在此基础上与均值一方差模型下求解的结果进行比较.     

Hawkes过程分支比估计——一种简单的非参数方法

Hawkes自激发过程是近年来被广泛用于金融建模的一个良好模型。本文提出了一种Hawkes自激发过程的分支比的简单估计方法,该方法是对Hardiman和Bouchaud提出的均值-方差估计量的改进。在继承均值-方差估计量形式简便的优点的同时,克服其参数难以选择的缺陷,减小了估计的系统性偏差。模拟结果验证了改进的效果,同时我们将该估计方法用于我国股市内生性水平的分析之中。     

大数据背景下网络调查样本的随机森林倾向得分模型推断研究

随着大数据与互联网技术的迅猛发展,网络调查的应用越来越广泛。本文提出网络调查样本的随机森林倾向得分模型推断方法,通过构建若干棵分类决策树组成随机森林,对网络调查样本单元的倾向得分进行估计,从而实现对总体的推断。模拟分析和实证研究结果表明:基于随机森林倾向得分模型的总体均值估计的相对偏差、方差与均方误差均比基于Logistic倾向得分模型的总体均值估计的相对偏差、方差与均方误差小,提出的方法估计效果更好。     

随机折现因子框架下均值-方差张成的计量分析

文章在随机折现因子的框架下对均值-方差张成问题进行了系统研究.首先,采用和Kan、Zhou(2001)不同的方法直接证明了新张成条件与现有张成条件的等价性;接着,探讨了新张成条件对应的检验模型的GMM估计及其Wald统计量的性质,通过Monte Carlo模拟揭示这些Wald统计量的小样本偏倚;最后,利用本文导出的均值-方差张成检验方法对中国股市进行实证研究.为了克服小样本偏倚的影响,文中采用Block-Bootstrap方法模拟了GMM估计的J统计量的分布.     

纵向部分线性变系数EV模型的估计

纵向数据是随着时间变化对个体进行重复观测而得到的一种相关性数据,广泛出现在诸多科学研究领域。在对个体进行观测时,测量误差不可避免,忽略测量误差往往会导致有偏估计。本文利用二次推断函数方法研究关于纵向数据的参数部分和非参数部分协变量均含有测量误差的部分线性变系数测量误差(errors-in-variables, EV)模型的估计问题。利用B样条逼近模型中的未知系数函数,构造关于回归参数和B样条系数的偏差修正的二次推断函数以处理个体内相关性和测量误差,得到回归参数和变系数的偏差修正的二次推断函数估计,然后证明了估计方法和结果的渐近性质。数值模拟和实例数据分析结果显示本文提出的方法具有一定的实用价值。     

一种异方差模型的两阶段估计

在异方差线性回归模型中,当模型误差项的协方差阵未知时,对异方差模型进行估计目前还没有比较好的方法。基于此,提出一种异方差模型的两阶段估计—基于异方差一致协方差阵估计,该方法将异方差一致协方差阵估计HC5m和广义最小二乘估计法结合起来,综合使用全部样本的信息,并对异方差模型进行估计。通过大量的蒙特卡洛数值模拟和实证分析,结果表明该方法具有一定的可行性和有效性。     

异方差模型参数估计的有效性研究

本文运用随机模拟方法,对误差序列异方差模型中加权最小二乘（GLS）估计的有效性进行研究。研究表明,GLS估计的有效性与异方差强度有关,当异方差强度较强时,GLS估计比普通最小二乘（OLS）估计有效;当异方差强度较弱时,GLS估计不如OLS估计有效。     

Stratified Double Sampling with Continuous Outcomes: Design and Analysis

We provide a method for estimating the sample mean of a continuous outcome in a stratified population using a double sampling scheme. The stratified sample mean is a weighted average of stratum specific means. It is assumed that the fallible and true outcome data are related by a simple linear regression model in each stratum. The optimal stratified double sampling plan, i.e. , the double sampling plan that minimizes the cost of sampling for fixed variances, or alternatively, minimizes the variance for fixed costs, is found and compared to a standard sampling plan. The design parameters are the total sample size and the number of doubly sampled units in each stratum. We show that the optimal double sampling plan is a function of the between-strata and within-strata cost and variance ratios. The efficiency gains, relative to standard sampling plans, under broad set of conditions, are considerable.     

Estimation of a rare sensitive attribute in a stratified two-stage unrelated randomized response model by using Poisson probability distribution

The present article deals with the estimation of mean number of respondents who possess a rare sensitive character in presence of known and unknown proportion of a rare unrelated non-sensitive attribute by using the Poisson probability distribution in stratified random sampling as well as in stratified random double sampling. The variance of rare sensitive character is also derived under proportional and optimal allocation methods in stratified random sampling when stratum sizes are known and unknown. The properties of the suggested estimation procedures have been deeply examined. The proposed model is found to be dominant over Lee et al. [Estimation of a rare sensitive attribute in a stratified sample using Poisson distribution. Statistics. 2013;47:575–589] model. Numerical illustrations are presented to support the theoretical results. Results are analysed and suitable recommendations are put forward to the survey practitioners.     

Hazard ratio inference in stratified clinical trials with time‐to‐event endpoints and limited sample size

The stratified Cox model is commonly used for stratified clinical trials with time‐to‐event endpoints. The estimated log hazard ratio is approximately a weighted average of corresponding stratum‐specific Cox model estimates using inverse‐variance weights; the latter are optimal only under the (often implausible) assumption of a constant hazard ratio across strata. Focusing on trials with limited sample sizes (50‐200 subjects per treatment), we propose an alternative approach in which stratum‐specific estimates are obtained using a refined generalized logrank (RGLR) approach and then combined using either sample size or minimum risk weights for overall inference. Our proposal extends the work of Mehrotra et al, to incorporate the RGLR statistic, which outperforms the Cox model in the setting of proportional hazards and small samples. This work also entails development of a remarkably accurate plug‐in formula for the variance of RGLR‐based estimated log hazard ratios. We demonstrate using simulations that our proposed two‐step RGLR analysis delivers notably better results through smaller estimation bias and mean squared error and larger power than the stratified Cox model analysis when there is a treatment‐by‐stratum interaction, with similar performance when there is no interaction. Additionally, our method controls the type I error rate while the stratified Cox model does not in small samples. We illustrate our method using data from a clinical trial comparing two treatments for colon cancer.     

Empirical Bayes estimation of undercount in the decennial census

Empirical Bayes methods are used to estimate the extent of the undercount at the local level in the 1980 U.S. census. "Grouping of like subareas from areas such as states, counties, and so on into strata is a useful way of reducing the variance of undercount estimators. By modeling the subareas within a stratum to have a common mean and variances inversely proportional to their census counts, and by taking into account sampling of the areas (e.g., by dual-system estimation), empirical Bayes estimators that compromise between the (weighted) stratum average and the sample value can be constructed. The amount of compromise is shown to depend on the relative importance of stratum variance to sampling variance. These estimators are evaluated at the state level (51 states, including Washington, D.C.) and stratified on race/ethnicity (3 strata) using data from the 1980 postenumeration survey (PEP 3-8, for the noninstitutional population)."     

A control in stratified sampling

A new expression of the variance of the units from a stratified finite population wit L strata, is obtained in funcions of the means L–1 strata, and in conseqeuence we obtained formulae which relates the mean of a stratum in a statistical study with the population mean and the ones of the remaining strate. As an application, we obtained a useful checking of the estimation consistency by stratified sampling in any precies survey     

A simulation study: estimation of population mean using two auxiliary variables in stratified random sampling

ABSTRACT

This paper deals with the problem of estimating the finite population mean in stratified random sampling by using two auxiliary variables. This paper proposed a ratio-cum-product exponential type estimator of population mean under different situations: (i) when there is presence of non-response and measurement errors on the study as well as auxiliary variables; (ii) when there is non-response on the study and auxiliary variables but with no measurement error; (iii) when there is complete response on study variable but there is presence of non-response and measurement error on the auxiliary variables and (iv) when there are complete response and measurement error on study as well as auxiliary variables. The expressions of the bias and mean square error of the proposed estimator have been obtained up to the first degree of approximation. The proposed estimator has been compared with usual unbiased estimator, ratio estimator and other existing estimators and the conditions obtained to show the efficacy of the proposed estimator over other considered estimators. Simulation study is carried out to support the theoretical findings.     

Trade-off between cost and variance for a multi-objective compromise allocation in stratified random sampling

In the present paper, a multi-objective goal optimization mechanism is developed by trading off between cost and variance. Both are adversaries to each other while allocating a sample size even in stratified sampling design. Discussion section shows how these adversaries put their influence on optimal selection. This is a dual optimization procedure in which variance or mean square error is optimized in the first step and then considering some compromise on variance, cost is optimized. The process is applied to both individual and multi-objective programming models.     

Estimation of finite population mean in stratified sampling using scrambled responses in the presence of measurement errors

This study focuses on the estimation of population mean of a sensitive variable in stratified random sampling based on randomized response technique (RRT) when the observations are contaminated by measurement errors (ME). A generalized estimator of population mean is proposed by using additively scrambled responses for the sensitive variable. The expressions for the bias and mean square error (MSE) of the proposed estimator are derived. The performance of the proposed estimator is evaluated both theoretically and empirically. Results are also applied to a real data set.     

Measurement error effect on the CUSUM control chart

The performance of the cumulative sum (CUSUM) control chart for the mean when measurement error exists is investigated. It is shown that the CUSUM chart is greatly affected by the measurement error. A similar result holds for the case of the CUSUM chart for the mean with linearly increasing variance. In this paper, we consider multiple measurements to reduce the effect of measurement error on the charts performance. Finally, a comparison of the CUSUM and EWMA charts is presented and certain recommendations are given.     

Estimating population characteristics by incorporating prior values in stratified random sampling/ranked set sampling

In this paper, we discuss the estimation of population characteristics using stratified random sampling in an infinite population framework, including ranked set sampling as a special case. The use of prior values is considered and the underlying distribution is assumed to be unknown. The estimator considered in each stratum is the weighted mean of the U-statistic and prior value. The optimum weight is obtained by minimizing the mean squared error of the estimator of the population characteristics, but it contains unknown parameters and those parameters are replaced with their estimates. Simulation results show the gains in efficiency of the proposed estimator, yielding gains of at least 1.2 times larger than the usual unbiased estimator under certain condition specified in the text. Guidelines for the usage of the proposed estimator are shown and an application to a real data set is provided.