连续性抽样调查中的样本轮换研究

 内容摘要：本文首先介?绍了样本轮换研究问题提出的背景和国内外研究现状。接着介绍了分层抽样下样本轮换的理论模型。包括分层抽样下样本轮换的估计量公式和最优样本轮换率的确定方法。再接着利用前面介绍的理论知识,结合上海市城镇住房空置率抽样调查数据进行实证分析。由于该抽样调查采取的是分层抽样,因此相应地用分层抽样下的样本轮换研究。先根据该抽样调查本身的特点和社会经济活动的规律确定样本轮换时间间隔为1年。再分别计算出各层的最优样本轮换率和总体的样本轮换率。最后分别对三层子总体样本轮换的效果进行分析,分析发现各层经过样本轮换以后的精度比不进行样本轮换或进行完全样本轮换的精度有了明显的提高,轮换效果显著。     

The population of the USSR

Official population data for the USSR for 1986 and 1987 are presented. Tables are included on age and sex distribution; rural and urban population; birth, death, and natural increase rates, 1970-1986; fertility and mortality by sex, 1970-1986; birth order; age-specific birth rates by rural and urban area and Union republic; age-specific death rates, 1970-1986; infant mortality, 1970-1986; life expectancy, 1926-1986; life tables; marriage and age at marriage; and divorce.     

The Use of Multiplicity in a Household Survey of Disabilities

The multiplicity technique has been proposed (Sirken, 1970) as a means of improving estimates of the number of rare “events” in a population. This paper describes one use of this technique, namely estimation of the number of persons with certain types of disability living in private dwellings in Canberra. The results are taken from three household surveys conducted in Canberra during 1978–79 in which a multiplicity rule linking parents, siblings and children of residents of sample households who were also living in private dwellings in Canberra was used. While no direct evidence on the level of non-sampling error is available here, it appears that net response errors at least are not substantial using this multiplicity rule and that a reasonable gain in sampling efficiency results from the use of multiplicity.     

Interval estimators for the population mean for skewed distributions with a small sample size

In finite population sampling, it has long been known that, for small sample sizes, when sampling from a skewed population, the usual frequentist intervals for the population mean cover the true value less often than their stated frequency of coverage. Recently, a non-informative Bayesian approach to some problems in finite population sampling has been developed, which is based on the 'Polya posterior'. For large sample sizes, these methods often closely mimic standard frequentist methods. In this paper, a modification of the 'Polya posterior', which employs the weighted Polya distribution, is shown to give interval estimators with improved coverage properties for problems with skewed populations and small sample sizes. This approach also yields improved tests for hypotheses about the mean of a skewed distribution.     

Robust extreme ranked set sampling

In this paper, a robust extreme ranked set sampling (RERSS) procedure for estimating the population mean is introduced. It is shown that the proposed method gives an unbiased estimator with smaller variance, provided the underlying distribution is symmetric. However, for asymmetric distributions a weighted mean is given, where the optimal weights are computed by using Shannon's entropy. The performance of the population mean estimator is discussed along with its properties. Monte Carlo simulations are used to demonstrate the performance of the RERSS estimator relative to the simple random sample (SRS), ranked set sampling (RSS) and extreme ranked set sampling (ERSS) estimators. The results indicate that the proposed estimator is more efficient than the estimators based on the traditional sampling methods.     

Multivariate shrinkage estimation of small area means and proportions

The familiar (univariate) shrinkage estimator of a small area mean or proportion combines information from the small area and a national survey. We define a multivariate shrinkage estimator which combines information also across subpopulations and outcome variables. The superiority of the multivariate shrinkage over univariate shrinkage, and of the univariate shrinkage over the unbiased (sample) means, is illustrated on examples of estimating the local area rates of economic activity in the subpopulations defined by ethnicity, age and sex. The examples use the sample of anonymized records of individuals from the 1991 UK census. The method requires no distributional assumptions but relies on the appropriateness of the quadratic loss function. The implementation of the method involves minimum outlay of computing. Multivariate shrinkage is particularly effective when the area level means are highly correlated and the sample means of one or a few components have small sampling and between-area variances. Estimations for subpopulations based on small samples can be greatly improved by incorporating information from subpopulations with larger sample sizes.     

Economically optimal markovian sampling policies for process monitoring

A variable delay process sampling procedure is considered in a Markov chain structure. The paper extends the basic sampling method given in Arnold (1970). Analytic properties of the process are developed for expected sample size and distribution of the sample size. A primary concern in the paper is the development of an objective function to enhance ability to select optimal sampling policies. The objective function involves cost due to sampling and protection costs for detecting undesirable conditions.     

Poverty and inequality in European regions

The European Union Statistics on Income and Living Conditions (EU-SILC) is the main source of information about poverty and economic inequality in the member states of the European Union. The sample sizes of its annual national surveys are sufficient for reliable estimation at the national level but not for inferences at the sub-national level, failing to respond to a rising demand from policy-makers and local authorities. We provide a comprehensive map of median income, inequality (Gini coefficient and Lorenz curve) and poverty (poverty rates) based on the equivalised household income in the countries in which the EU-SILC is conducted. We study the distribution of income of households (pro-rated to its members), not merely its median (or mean), because we regard its dispersion and frequency of lower extremes (relative poverty) as important characteristics. The estimation for the regions with small sample sizes is improved by the small-area methods. The uncertainty of complex nonlinear statistics is assessed by bootstrap. Household-level sampling weights are taken into account in both the estimates and the associated bootstrap standard errors.     

Constructing quantile confidence intervals using extended simple random sample in finite populations

This paper constructs quantile confidence intervals based on extended simple random sample (SRS) from a finite population, where ranks of population units are all known. Extended simple random sample borrows additional information from unmeasured observations in the population by conditioning on the population ranks of the measured units in SRS. The confidence intervals are improved using Rao-Blackwell theorem over the conditional distribution of sample ranks given the measured sample units. Empirical evidence shows that the proposed confidence intervals have shorter lengths than confidence intervals constructed from an SRS sample.     

Posterior Distributions for the Gini Coefficient Using Grouped Data

When available data comprise a number of sampled households in each of a number of income classes, the likelihood function is obtained from a multinomial distribution with the income class population proportions as the unknown parameters. Two methods for going from this likelihood function to a posterior distribution on the Gini coefficient are investigated. In the first method, two alternative assumptions about the underlying income distribution are considered, namely a lognormal distribution and the Singh–Maddala (1976) income distribution. In these cases the likelihood function is reparameterized and the Gini coefficient is a nonlinear function of the income distribution parameters. The Metropolis algorithm is used to find the corresponding posterior distributions of the Gini coefficient from a sample of Bangkok households. The second method does not require an assumption about the nature of the income distribution, but uses (a) triangular prior distributions, and (b) beta prior distributions, on the location of mean income within each income class. By sampling from these distributions, and the Dirichlet posterior distribution of the income class proportions, alternative posterior distributions of the Gini coefficient are calculated.     

QUALITY ISSUES IN TELEPHONE SURVEYS: COVERAGE, NON-RESPONSE and QUOTA SAMPLING

The quality of a telephone survey is affected by several factors: telephone coverage, non-response, the methods used to select households and persons, and the quality of responses obtained from respondents. Data are provided which show that a large proportion of Australian households have telephone connections. However, telephone coverage is not uniform and some subgroups of the population have much lower connection rates. This paper reviews evidence of the effect of non-response and the effectiveness of repeated call backs, and reports the results of a new study. The use of quota sampling to select respondents from randomly selected households is also examined. The results suggest that telephone surveys under-represent older persons and the unemployed, and over-represent middle-aged persons. It is shown that while call backs can increase the response rate, the effect on the composition of the sample and resulting estimates is minimal. The main effects are due to refusals and variation in coverage rates.     

Variance Estimators of the Gini Coefficient—Probability Sampling

An estimator of the Gini coefficient (the well-known income inequality measure) of a finite population is defined for an arbitrary probability sampling design, taking the sampling design into consideration. Alternative estimators of the variance of the estimated Gini coefficient are introduced. The sampling performance of the Gini coefficient estimator and its variance estimators is studied by means of a Monte Carlo study, using stratified sampling from a miniature population of Swedish households with authentic income data.     

Spatially Balanced Sampling of Continuous Populations

When sampling from a continuous population (or distribution), we often want a rather small sample due to some cost attached to processing the sample or to collecting information in the field. Moreover, a probability sample that allows for design‐based statistical inference is often desired. Given these requirements, we want to reduce the sampling variance of the Horvitz–Thompson estimator as much as possible. To achieve this, we introduce different approaches to using the local pivotal method for selecting well‐spread samples from multidimensional continuous populations. The results of a simulation study clearly indicate that we succeed in selecting spatially balanced samples and improve the efficiency of the Horvitz–Thompson estimator.     

Designing stratified sampling in economic and business surveys

In most economic and business surveys, the target variables (e.g. turnover of enterprises, income of households, etc.) commonly resemble skewed distributions with many small and few large units. In such surveys, if a stratified sampling technique is used as a method of sampling and estimation, the convenient way of stratification such as the use of demographical variables (e.g. gender, socioeconomic class, geographical region, religion, ethnicity, etc.) or other natural criteria, which is widely practiced in economic surveys, may fail to form homogeneous strata and is not much useful in order to increase the precision of the estimates of variables of interest. In this paper, a stratified sampling design for economic surveys based on auxiliary information has been developed, which can be used for constructing optimum stratification and determining optimum sample allocation to maximize the precision in estimate.     

Exact Bayesian Inference and Model Selection for Stochastic Models of Epidemics Among a Community of Households

Abstract.  Much recent methodological progress in the analysis of infectious disease data has been due to Markov chain Monte Carlo (MCMC) methodology. In this paper, it is illustrated that rejection sampling can also be applied to a family of inference problems in the context of epidemic models, avoiding the issues of convergence associated with MCMC methods. Specifically, we consider models for epidemic data arising from a population divided into households. The models allow individuals to be potentially infected both from outside and from within the household. We develop methodology for selection between competing models via the computation of Bayes factors. We also demonstrate how an initial sample can be used to adjust the algorithm and improve efficiency. The data are assumed to consist of the final numbers ultimately infected within a sample of households in some community. The methods are applied to data taken from outbreaks of influenza.     

On prediction of population and subpopulation characteristics for future periods

The estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.     

Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering

SUMMARY Ranked-set sampling is a widely used sampling procedure when sample observations are expensive or difficult to obtain. It departs from simple random sampling by seeking to spread the observations in the sample widely over the distribution or population. This is achieved by ranking methods which may need to employ concomitant information. The ranked-set sample mean is known to be more efficient than the corresponding simple random sample mean. Instead of the ranked-set sample mean, this paper considers the corresponding optimal estimator: the ranked-set best linear unbiased estimator. This is shown to be more efficient, even for normal data, but particularly for skew data, such as from an exponential distribution. The corresponding forms of the estimators are quite distinct from the ranked-set sample mean. Improvement holds where the ordering is perfect or imperfect, with this prospect of improper ordering being explored through the use of concomitants. In addition, the corresponding optimal linear estimator of a scale parameter is also discussed. The results are applied to a biological problem that involves the estimation of root weights for experimental plants, where the expense of measurement implies the need to minimize the number of observations taken.     

A review of nonparametric ranked-set sampling methodology

Ranked-set sampling is an alternative to random sampling for settings in which measurements are difficult or costly. Ranked-set sampling utilizes information gained without measurement to structure the eventual measured sample. This additional information yields improved properties for ranked-set sample procedures relative to their simple random sample counterparts. We review the available nonparametric procedures for data from ranked-set samples. Estimation of the distribution function was the first nonparametric setting to which ranked-set sampling methodology was applied. Since the first paper on the ranked-set sample empirical distribution function, the two-sample location setting, the sign test, and the signed-rank test have all been examined for ranked-set samples. In addition, estimation of the distribution function has been considered in a more general setting. We discuss the similarities and differences in the properties of the ranked-set sample procedures for the various settings     

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.     

Inverse Adaptive Cluster Sampling with Unequal Selection Probabilities: Case Studies on Crab Holes and Arsenic Pollution

Adaptive cluster sampling is an efficient method of estimating the parameters of rare and clustered populations. The method mimics how biologists would like to collect data in the field by targeting survey effort to localised areas where the rare population occurs. Another popular sampling design is inverse sampling. Inverse sampling was developed so as to be able to obtain a sample of rare events having a predetermined size. Ideally, in inverse sampling, the resultant sample set will be sufficiently large to ensure reliable estimation of population parameters. In an effort to combine the good properties of these two designs, adaptive cluster sampling and inverse sampling, we introduce inverse adaptive cluster sampling with unequal selection probabilities. We develop an unbiased estimator of the population total that is applicable to data obtained from such designs. We also develop numerical approximations to this estimator. The efficiency of the estimators that we introduce is investigated through simulation studies based on two real populations: crabs in Al Khor, Qatar and arsenic pollution in Kurdistan, Iran. The simulation results show that our estimators are efficient.