An effective hybrid variance reduction method for pricing the Asian options and its variants

In this paper, we propose a variance reduction method that combines importance sampling and control variates to price European Arithmetic Asian options and its variants (i.e., Asian options plus knock-in or knock-out options) under the Black-Scholes model. The numerical results show that the proposed methods are especially efficient under the following scenarios: in the money, low volatility, more sampling dates, and higher barrier thresholds.     

General framework for the rotation of units in repeated survey sampling

Coordination of probabilistic samples is a challenging theoretical problem faced by statistical institutes. One of their aims is to obtain good estimates for each wave while spreading the response burden across the entire population. There is a collection of existing solutions that try to attend to these needs. These solutions, which were developed independently, are integrated in a general framework and their corresponding longitudinal designs are computed. The properties of these longitudinal designs are discussed. It is also noted that there is an antagonism between a good rotation and control over the cross-sectional sampling design. A compromise needs to be reached between the quality of the sample coordination, which appears to be optimal for a systematic longitudinal sampling design, and the freedom of choice of the cross-sectional design. In order to reach such a compromise, an algorithm that uses a new method of longitudinal sampling is proposed.     

双侧限“σ”法抽样方案的设计（均值）——关于GB／T8054—2008表2的设计建议

文章利用文献[1]中的理论公式和数据表，给出了以均值为质量指标的双侧限“σ”法抽样方案表。该抽样方案表的设计是对GB／T8054—2008表2的改进，不仅符合设计目标，而且更便于应用。     

科技文献中标点符号的正确用法

标点符号在科技工程界的书面语言中是十分重要的。为此，根据ＧＢ／Ｔ１５８３４－１９９５《标点符号用法》，结合工作经验，阐述了标点符号在科技文献中的正确用法     

抽检国标路线图

本文将16个抽检国标，主要基于计数与计量、孤立与连续的分类，归纳成便于检索的路线图。对类似抽检问题，比较了众多不同抽检国标的方案，并举例说明百分比抽检不合理。     

Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

In survey sampling, auxiliary information on the population is often available. The aim of this paper is to develop a method which allows one to take into account such auxiliary information at the estimation stage by means of conditional bias adjustment. The basic idea is to attempt to construct a conditionally unbiased estimator. Four estimators that have a small conditional bias with respect to a statistic are proposed. It is shown that many of the estimators used in the literature in the case of simple random sampling can be obtained by using this estimation principle. The problem of simple random sampling with replacement, poststratification, and adjustment of a 2 x 2 dimensional contingency table to marginal totals are discussed in the conditional framework. Finally it is shown that the regression estimator can be viewed as an approximation of an application of the conditional principle.     

Credit to and in acceptance sampling

A simple method of controlling average outgoing quality is discussed. It is based on a straightforward definition of credit and proved to be valid under a quite tractable condition. The special case of acceptance sampling by attributes is studied in detail.     

Mixed random systematic sampling designs

In this paper, an alternative sampling procedure that is a mixture of simple random sampling and systematic sampling is proposed. It results in uniform inclusion probabilities for all individual units and positive inclusion probabilities for all pairs of units. As a result, the proposed sampling procedure enables us to estimate the population mean unbiasedly using the ordinary sample mean, and to provide an unbiased estimator of its sampling variance. It is also found that the suggested sampling procedure performs well especially when the size of simple random sample is small. Received August 2001     

A Destructive Sampling Method Designed for Outsourcing Situations Involving High Quality Production Processes

In outsourcing situations involving manufacturing and assembly, the sampling of units produced is important since in many situations not all of the units can be tested. Destructive sampling, which commonly occurs in the assembly and manufacturing industry, is a form of sampling where all units produced cannot be tested since the parts are destructively tested. In this situation, sampling techniques are used to determine if an entire lot should be accepted or rejected based on the sampling results. The traditional sampling techniques include single or classical sampling, double sampling, multiple sampling, skip-lot sampling, chain sampling and MIL-STD-105E. The purpose of this paper is to develop a sophisticated technique that monitors quality at a lower cost than traditional methods yet has similar monitoring characteristics in situations where quality is high and tests are destructive. The proposed technique, Destructive Sampling Method for High Quality production processes (DSM-HQ), is based on a cost function, which balances the costs of sampling versus the costs of finding a defect on the field. DSM-HQ assumes to have a Poisson process defect pattern and uses an Empirical Bayesian analysis to allow the researcher to include prior knowledge.     

Uncertainty Estimation for Pseudo‐Bayesian Inference Under Complex Sampling

Social and economic studies are often implemented as complex survey designs. For example, multistage, unequal probability sampling designs utilised by federal statistical agencies are typically constructed to maximise the efficiency of the target domain level estimator (e.g. indexed by geographic area) within cost constraints for survey administration. Such designs may induce dependence between the sampled units; for example, with employment of a sampling step that selects geographically indexed clusters of units. A sampling‐weighted pseudo‐posterior distribution may be used to estimate the population model on the observed sample. The dependence induced between coclustered units inflates the scale of the resulting pseudo‐posterior covariance matrix that has been shown to induce under coverage of the credibility sets. By bridging results across Bayesian model misspecification and survey sampling, we demonstrate that the scale and shape of the asymptotic distributions are different between each of the pseudo‐maximum likelihood estimate (MLE), the pseudo‐posterior and the MLE under simple random sampling. Through insights from survey‐sampling variance estimation and recent advances in computational methods, we devise a correction applied as a simple and fast postprocessing step to Markov chain Monte Carlo draws of the pseudo‐posterior distribution. This adjustment projects the pseudo‐posterior covariance matrix such that the nominal coverage is approximately achieved. We make an application to the National Survey on Drug Use and Health as a motivating example and we demonstrate the efficacy of our scale and shape projection procedure on synthetic data on several common archetypes of survey designs.     

现浇空心楼盖GBF管质量检查及抽样方法探讨

GBF管的质量检查和验收是现浇空心楼板质量控制的关键,包括GBF管材料、制作和施工等多方面内容,而抽样检测又是GBF管质量检查验收的重要手段,本文对监理工程师基于空心楼板GBF管质量检查的内容及抽样检测方法进行了分析和探讨。     

Modified efficient importance sampling for partially non‐Gaussian state space models

The construction of an importance density for partially non‐Gaussian state space models is crucial when simulation methods are used for likelihood evaluation, signal extraction, and forecasting. The method of efficient importance sampling is successful in this respect, but we show that it can be implemented in a computationally more efficient manner using standard Kalman filter and smoothing methods. Efficient importance sampling is generally applicable for a wide range of models, but it is typically a custom‐built procedure. For the class of partially non‐Gaussian state space models, we present a general method for efficient importance sampling. Our novel method makes the efficient importance sampling methodology more accessible because it does not require the computation of a (possibly) complicated density kernel that needs to be tracked for each time period. The new method is illustrated for a stochastic volatility model with a Student's t distribution.     

A threshold stochastic volatility model with explanatory variables

In this paper, we introduce a threshold stochastic volatility model with explanatory variables. The Bayesian method is considered in estimating the parameters of the proposed model via the Markov chain Monte Carlo (MCMC) algorithm. Gibbs sampling and Metropolis–Hastings sampling methods are used for drawing the posterior samples of the parameters and the latent variables. In the simulation study, the accuracy of the MCMC algorithm, the sensitivity of the algorithm for model assumptions, and the robustness of the posterior distribution under different priors are considered. Simulation results indicate that our MCMC algorithm converges fast and that the posterior distribution is robust under different priors and model assumptions. A real data example was analyzed to explain the asymmetric behavior of stock markets.     

连续批计数抽样检验中的跳批抽样技术

文章介绍了跳批抽样的基本原理、适用范围、条件以及一般程序。文章主要对GB／T2828．3《计数抽样检验程序第3部分跳批抽样程序》技术内容进行了解读和介绍,帮助实际应用者正确运用跳批抽样程序,以达到预期目的。     

一种新型的计量型抽样检验方法——三样本检验法

许多公司的进料检验面临检验效率低下、检验价值丧失的困境,如何提升进料检验的效率并促进进料检验发挥有价值的效用是一个现实的课题。文章针对计量型质量特性所提出的三样本检验法是一种新型的计量型抽样检验方法,希望能够为帮助企业走出进料检验的困境发挥效用。     

Mean square error estimation in multi-stage sampling

Summary: Suppose for a homogeneous linear unbiased function of the sampled first stage unit (fsu)-values taken as an estimator of a survey population total, the sampling variance is expressed as a homogeneous quadratic function of the fsu-values. When the fsu-values are not ascertainable but unbiased estimators for them are separately available through sampling in later stages and substituted into the estimator, Raj (1968) gave a simple variance estimator formula for this multi-stage estimator of the population total. He requires that the variances of the estimated fsu-values in sampling at later stages and their unbiased estimators are available in certain `simple forms'. For the same set-up Rao (1975) derived an alternative variance estimator when the later stage sampling variances have more ‘complex forms’. Here we pursue with Raj's (1968) simple forms to derive a few alternative variance and mean square error estimators when the condition of homogeneity or unbiasedness in the original estimator of the total is relaxed and the variance of the original estimator is not expressed as a quadratic form.  We illustrate a particular three-stage sampling strategy and present a simulation-based numerical exercise showing the relative efficacies of two alternative variance estimators. Received: 19 February 1999     

Bayesian inference in time series models using kernel quasi likelihoods

The paper takes up Bayesian inference in time series models when essentially nothing is known about the distribution of the dependent variable given past realizations or other covariates. It proposes the use of kernel quasi likelihoods upon which formal inference can be based. Gibbs sampling with data augmentation is used to perform the computations related to numerical Bayesian analysis of the model. The method is illustrated with artificial and real data sets.     

Estimation of the mean in ranked set sampling with non responses

The estimation of the population mean when ranked set sampling [rss] is used for selecting the sample and non responses [nr] are present, is studied. The nr stratum is sub sampled using simple random sampling with replacement. Two strategies are analyzed. One of them is based on the selection of a sub sample from the nr in each cycle. The other uses sub samples selected among the nr in each rank.  The accuracy of the proposed estimators is characterized by the corresponding expected variances. Simulations and real life data are used for analyzing the behavior of them. Acknowledgements: This paper was developed partially during the visit of the author to Université des Antilles et Gouyane. The author gratefully acknowledges the helpful suggestions of the referees and thanks the support of DAAD for visiting Humboldt University where a version of the paper version was made.     

A Guide to Exact Simulation

Markov Chain Monte Carlo (MCMC) methods are used to sample from complicated multivariate distributions with normalizing constants that may not be computable in practice and from which direct sampling is not feasible. A fundamental problem is to determine convergence of the chains. Propp & Wilson (1996) devised a Markov chain algorithm called Coupling From The Past (CFTP) that solves this problem, as it produces exact samples from the target distribution and determines automatically how long it needs to run. Exact sampling by CFTP and other methods is currently a thriving research topic. This paper gives a review of some of these ideas, with emphasis on the CFTP algorithm. The concepts of coupling and monotone CFTP are introduced, and results on the running time of the algorithm presented. The interruptible method of Fill (1998) and the method of Murdoch & Green (1998) for exact sampling for continuous distributions are presented. Novel simulation experiments are reported for exact sampling from the Ising model in the setting of Bayesian image restoration, and the results are compared to standard MCMC. The results show that CFTP works at least as well as standard MCMC, with convergence monitored by the method of Raftery & Lewis (1992, 1996).     

Cross-sectional surveys: Inferring total eventual time in current state using only elapsed time-to-date

We focus on snapshot surveying of sub-populations whose members are in a temporary state and where one of the questions asked is the elapsed time already spent in that state. From these answers we develop probabilistic and statistical procedures to estimate the distribution of total time that will eventually be spent in that state by any random individual who enters the state. The method relies on a selection bias often found in temporal sampling, sometimes called “random incidence” or “longevity bias.” We develop results for several types of sampling, including random and fixed times of surveying, random and fixed times of entering the state, and sampling only those who have already spent some minimal specified time in the targeted state. An example with post-doc data is included to demonstrate the steps.