A New Sampling Design for Systematic Sampling

A sampling design called “Modified Systematic Sampling (MSS)” is proposed. In this design each unit has an equal probability of selection. Moreover, it works for both situations: N = nk or N ≠ nk. Consequently, the Linear Systematic Sampling (LSS) and Circular Systematic Sampling (CSS) become special cases of the proposed MSS design.     

Star-Type Systematic Sampling Schemes for Finite Populations

Two new sampling schemes namely, Star-Type Systematic (STS) sampling without replacement and Modified Star-Type Systematic (MSTS) sampling without replacement for estimation of finite population means are introduced. The relative performances of the proposed star-type systematic sample means along with those of the simple random and systematic sample means are assessed for a hypothetical population with a linear trend and also for certain natural populations. Furthermore, the usefulness of the proposed sampling schemes in quality control and for constructing partial diallel crosses in mating designs are briefly break discussed.     

对称等距抽样问题浅析

各种版本的《统计学原理》教材对对称等距抽样的表述不一致。本文分析了各种教材的各种论述,并期望探索出对称等距抽样更为精确的表达方式。     

中国农产量调查中几种可行的PPS系统抽样设计

PPS系统抽样设计是国际上比较流行的设计,它在实践中有着广泛的应用。我国农产量调查采用的是对称等距抽样设计,它实际上可理解为是一种变形的PPS系统抽样设计,使用的是以播种面积作为辅助变量。文章给出了几种可行的PPS系统抽样设计,辅助变量分别取为农户数、播种面积、耕地面积、切块数,并对这几种抽样设计进行了应用分析。     

Some remarks on the traditional way of circular and diagonal circular systematic sampling schemes

ABSTRACT

In this paper, some deficiencies in traditional selection procedure of circular version of systematic sampling schemes are investigated and alternative methods are proposed. We also suggest some rules of thumb for coincidence of units in the sample. The end corrections proposed by Bellhouse and Rao (1975 Bellhouse, D.R., Rao, J.N.K. (1975). Systematic sampling in the presence of a trend. Biometrika. 62:694–697.[Crossref], [Web of Science ®] , [Google Scholar]) and Sampath and Varalakshmi (2008) for circular systematic sampling and diagonal circular systematic sampling, respectively, are also modified.     

Estimation of Population Mean in the Presence of Linear Trend

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.     

Comparison of methods for analyzing binary repeated measures data: A simulation-based study (comparison of methods for binary repeated measures)

In this study, some methods suggested for binary repeated measures, namely, Weighted Least Squares (WLS), Generalized Estimating Equations (GEE), and Generalized Linear Mixed Models (GLMM) are compared with respect to power, type 1 error, and properties of estimates. The results indicate that with adequate sample size, no missing data, the only covariate being time effect, and a relatively limited number of time points, the WLS method performs well. The GEE approach performs well only for large sample sizes. The GLMM method is satisfactory with respect to type I error, but its estimates have poorer properties than the other methods.     

Multiple-start balanced modified systematic sampling in the presence of linear trend

ABSTRACT

In this paper, we propose a sampling design termed as multiple-start balanced modified systematic sampling (MBMSS), which involves the supplementation of two or more balanced modified systematic samples, thus permitting us to obtain an unbiased estimate of the associated sampling variance. There are five cases for this design and in the presence of linear trend only one of these cases is optimal. To further improve results for the other cases, we propose an estimator that removes linear trend by applying weights to the first and last sampling units of the selected balanced modified systematic samples and is thus termed as the MBMSS with end corrections (MBMSSEC) estimator. By assuming a linear trend model averaged over a super-population model, we will compare the expected mean square errors (MSEs) of the proposed sample means, to that of simple random sampling (SRS), linear systematic sampling (LSS), stratified random sampling (STR), multiple-start linear systematic sampling (MLSS), and other modified MLSS estimators. As a result, MBMSS is optimal for one of the five possible cases, while the MBMSSEC estimator is preferred for three of the other four cases.     

Remainder Markov systematic sampling

Systematic sampling is the simplest and easiest of the most common sampling methods. However, when the population size N cannot be evenly divided by the sampling size n, systematic sampling cannot be performed. Not only is it difficult to determine the sampling interval k equivalent to the sampling probability of the sampling unit, but also the sample size will be inconstant and the sample mean will be a biased estimator of the population mean. To solve this problem, this paper introduces an improved method for systematic sampling: the remainder Markov systematic sampling method. This new method involves separately finding the first-order and second-order inclusion probabilities. This approach uses the Horvitz-Thompson estimator as an unbiased estimator of the population mean to find the variance of the estimator. This study examines the effectiveness of the proposed method for different super-populations.     

Spatial sampling in the presence of a trend

The spatial sampling designs suggested by Quenouille (1949) are investigated under a number of trend assumptions, namely a linear trend, linear trend and periodic variation, and spatially correlated populations. The results obtained provide a planar analogue to the one-dimensional results appearing in Cochram (1977, Ch. ε). Centrally located systematic sampling and the planar analogue of Yates' (1948) method of end corrections are put forward as methods which eliminate the linear trend. The comparisons of the two methods provide the planar analogue to results obtained by Bellhouse and Rao (1975).     

Estimation of the mean of the exponential distribution using moving extremes ranked set sampling

Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).     

中国广义回归抽样估计系统的构建及应用

在抽样理论和应用研究方面,中国一直比较重视抽样方案设计,而忽视抽样估计方法研究。本文在系统总结加拿大等西方国家成功经验的基础上,引入并改进了一套广义回归估计系统,应用在复杂的连续多阶抽样调查中。本文以各类常见的抽样设计为基础,通过模型组和模型水平将现有的超总体模型进行扩展,建立各种类型的回归模型进行模型辅助的广义回归估计,最终形成一套广义回归估计系统,为中国抽样估计的应用研究奠定理论基础。最后,本文以中国农产量的连续多阶抽样调查为例,给出了具体的回归估计程序,从而验证这套系统的实践性和应用价值。     

Regenerative Markov Chain Importance Sampling

We introduce Markov Chain Importance Sampling (MCIS), which combines importance sampling (IS) and Markov Chain Monte Carlo (MCMC) to estimate some characteristics of a non-normalized multi-dimensional distribution. Especially, we introduce some importance functions whose variates are regeneratively generated by MCMC; these variates then are used to estimate the quantity of interest through IS. Because MCIS is regenerative, it overcomes the burn-in problem associated with MCMC. It could also speed up the mixing rate in MCMC.     

Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Optimization of design parameters for control charts with multiple assignable causes

Duncan's economic model of Shewhart's original x¯ chart has established its optimal and economic application for processes with the Markovian failure characteristic. As the sample statistics show some indications of process variations, the variable-sampling-interval (VSI) control charts perform more effectively than the fixed sampling interval (FSI) ones due to a higher frequency in the sampling rate. Regarding the economic design of control charts, most studies have been dedicated to the FSI scheme. In 1998, Bai & Lee considered the production process with a single assignable cause and proposed an economic VSI design for a general x¯ control chart. However, in real cases, there are multiple assignable causes in the production process. Therefore, concerning the operation characteristics of the real industry, this research develops an economic model for the VSI control chart with multiple assignable causes based on stochastic and statistics theory and determines the optimal design parameters of the chart. A numerical example is also provided to demonstrate the effectiveness of the proposed model and the result indicates that VSI performs more effectively than a FSI control chart.     

Parameter expansion for sampling a correlation matrix: an efficient GPX-RPMH algorithm

Sampling the correlation matrix (R) plays an important role in statistical inference for correlated models. There are two main constraints on a correlation matrix: positive definiteness and fixed diagonal elements. These constraints make sampling R difficult. In this paper, an efficient generalized parameter expanded re-parametrization and Metropolis-Hastings (GPX-RPMH) algorithm for sampling a correlation matrix is proposed. Drawing all components of R simultaneously from its full conditional distribution is realized by first drawing a covariance matrix from the derived parameter expanded candidate density (PXCD), and then translating it back to a correlation matrix and accepting it according to a Metropolis-Hastings (M-H) acceptance rate. The mixing rate in the M-H step can be adjusted through a class of tuning parameters embedded in the generalized candidate prior (GCP), which is chosen for R to derive the PXCD. This algorithm is illustrated using multivariate regression (MVR) models and a simulation study shows that the performance of the GPX-RPMH algorithm is more efficient than that of other methods.     

Remainder modified systematic sampling in the presence of linear trend

If the population size is not a multiple of the sample size, then the usual linear systematic sampling design is unattractive, since the sample size obtained will either vary, or be constant and different to the required sample size. Only a few modified systematic sampling designs are known to deal with this problem and in the presence of linear trend, most of these designs do not provide favorable results. In this paper, a modified systematic sampling design, known as remainder modified systematic sampling (RMSS), is introduced. There are seven cases of RMSS and the results in this paper suggest that the proposed design is favorable, regardless of each case, while providing linear trend-free sampling results for three of the seven cases. To obtain linear trend-free sampling for the other cases and thus improve results, an end corrections estimator is constructed.     

中国价格型货币政策的系统性与非系统性时变效应研究

本文建立兼具随机波动率和时变参数的VAR模型,刻画经济系统中结构冲击和传导机制的时变性,并在同一框架内分析价格型货币政策的系统性和非系统性效应。研究结果显示：（1）对应于货币政策冲击,货币政策的非系统性效应在大波动时期存在“价格之谜”现象,在大稳定时期则出现政策冲击波动以及经济活动对其同向响应程度的双重下降现象,甚至在有些时段出现负向响应,其平抑经济波动的作用得到一定程度的体现。（2）系统性效应显示货币政策对于通货膨胀的响应强度整体呈消极特征,但存在一种往积极方向转变的动态学习模式,而且这种转变呈现不同状态的频繁转换。（3）反事实分析显示货币政策系统性和非系统性效应虽然有所改善,但这并不是宏观经济从大波动向大稳定转变的主要原因。