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Population Total (population + total)

Distribution by Scientific Domains

Mathematics and Statistics	83%

Selected Abstracts

A General Algorithm for Univariate Stratification

INTERNATIONAL STATISTICAL REVIEW, Issue 3 2009
Sophie Baillargeon
Summary This paper presents a general algorithm for constructing strata in a population using,X, a univariate stratification variable known for all the units in the population. Stratum,h,consists of all the units with an,X,value in the interval[bh,1,,bh). The stratum boundaries{bh}are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable,Y,with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable,X,and the survey variable,Y. A loglinear model with stratum-specific mortality for,Y,given,X,is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification, an R package that will be available on CRAN (Comprehensive R Archive Network). Résumé Cet article présente un algorithme général pour construire des strates dans une population à l'aide de,X, une variable de stratification unidimensionnelle connue pour toutes les unités de la population. La strate,h,contient toutes les unités ayant une valeur de,X,dans l'intervalle [bh,1,,bh). Les frontières des strates {bh} sont obtenues en minimisant la taille d'échantillon anticipée pour l'estimation du total de la variable d'intérêt,Y,avec un niveau de précision prédéterminé. Le critère de stratification permet la présence d'une strate à tirage nul et de strates recensement. L'échantillon est réparti dans les strates à l'aide d'une règle générale qui inclut l'allocation proportionnelle, l'allocation de Neyman et l'allocation de puissance comme des cas particuliers. L'optimisation peut tenir compte d'un taux de non réponse spécifique à la strate et d'un modèle reliant la variable de stratification,X,à la variable d'intérêt,Y. Un modèle loglinéaire avec un taux de mortalité propre à la strate est présenté en détail. Deux algorithmes numériques pour déterminer les frontières de strates optimales, dus à Sethi et Kozak, sont comparés dans une étude numérique. Plusieurs exemples illustrent les plans stratifiés qui peuvent être construits avec la méthodologie proposée. Tous les calculs présentés dans l'article ont été effectués avec stratification, un package R disponible auprès des auteurs. [source]

Sampling within households in household surveys

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES A (STATISTICS IN SOCIETY), Issue 1 2007
Robert G. Clark
Summary., The number of people to select within selected households has significant consequences for the conduct and output of household surveys. The operational and data quality implications of this choice are carefully considered in many surveys, but the effect on statistical efficiency is not well understood. The usual approach is to select all people in each selected household, where operational and data quality concerns make this feasible. If not, one person is usually selected from each selected household. We find that this strategy is not always justified, and we develop intermediate designs between these two extremes. Current practices were developed when household survey field procedures needed to be simple and robust; however, more complex designs are now feasible owing to the increasing use of computer-assisted interviewing. We develop more flexible designs by optimizing survey cost, based on a simple cost model, subject to a required variance for an estimator of population total. The innovation lies in the fact that household sample sizes are small integers, which creates challenges in both design and estimation. The new methods are evaluated empirically by using census and health survey data, showing considerable improvement over existing methods in some cases. [source]

VARIANCE ESTIMATION IN TWO-PHASE SAMPLING

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
M.A. Hidiroglou
Summary Two-phase sampling is often used for estimating a population total or mean when the cost per unit of collecting auxiliary variables, x, is much smaller than the cost per unit of measuring a characteristic of interest, y. In the first phase, a large sample s1 is drawn according to a specific sampling design p(s1), and auxiliary data x are observed for the units i,s1. Given the first-phase sample s1, a second-phase sample s2 is selected from s1 according to a specified sampling design {p(s2,s1) }, and (y, x) is observed for the units i,s2. In some cases, the population totals of some components of x may also be known. Two-phase sampling is used for stratification at the second phase or both phases and for regression estimation. Horvitz,Thompson-type variance estimators are used for variance estimation. However, the Horvitz,Thompson (Horvitz & Thompson, J. Amer. Statist. Assoc. 1952) variance estimator in uni-phase sampling is known to be highly unstable and may take negative values when the units are selected with unequal probabilities. On the other hand, the Sen,Yates,Grundy variance estimator is relatively stable and non-negative for several unequal probability sampling designs with fixed sample sizes. In this paper, we extend the Sen,Yates,Grundy (Sen, J. Ind. Soc. Agric. Statist. 1953; Yates & Grundy, J. Roy. Statist. Soc. Ser. B 1953) variance estimator to two-phase sampling, assuming fixed first-phase sample size and fixed second-phase sample size given the first-phase sample. We apply the new variance estimators to two-phase sampling designs with stratification at the second phase or both phases. We also develop Sen,Yates,Grundy-type variance estimators of the two-phase regression estimators that make use of the first-phase auxiliary data and known population totals of some of the auxiliary variables. [source]

Ratio Estimation with Measurement Error in the Auxiliary Variate

BIOMETRICS, Issue 2 2009
Timothy G. Gregoire
Summary With auxiliary information that is well correlated with the primary variable of interest, ratio estimation of the finite population total may be much more efficient than alternative estimators that do not make use of the auxiliary variate. The well-known properties of ratio estimators are perturbed when the auxiliary variate is measured with error. In this contribution we examine the effect of measurement error in the auxiliary variate on the design-based statistical properties of three common ratio estimators. We examine the case of systematic measurement error as well as measurement error that varies according to a fixed distribution. Aside from presenting expressions for the bias and variance of these estimators when they are contaminated with measurement error we provide numerical results based on a specific population. Under systematic measurement error, the biasing effect is asymmetric around zero, and precision may be improved or degraded depending on the magnitude of the error. Under variable measurement error, bias of the conventional ratio-of-means estimator increased slightly with increasing error dispersion, but far less than the increased bias of the conventional mean-of-ratios estimator. In similar fashion, the variance of the mean-of-ratios estimator incurs a greater loss of precision with increasing error dispersion compared with the other estimators we examine. Overall, the ratio-of-means estimator appears to be remarkably resistant to the effects of measurement error in the auxiliary variate. [source]

VARIANCE ESTIMATION IN TWO-PHASE SAMPLING

ACCOUNTING FOR POPULATION AGEING IN TAX MICROSIMULATION MODELLING BY SURVEY REWEIGHTING,

AUSTRALIAN ECONOMIC PAPERS, Issue 1 2006
LIXIN CAI
This paper investigates the use of sample reweighting, in a behavioural tax microsimulation model, to examine the implications for government taxes and expenditure of population ageing in Australia. First, a calibration approach to sample reweighting is described, producing new weights that achieve specified population totals for selected variables. Second, the performance of the Australian Bureau of Statistics' (ABS) weights provided with the 2000,2001 Survey of Income and Housing Cost (SIHC) was examined and it was found that reweighting does not improve the simulation outcomes for the 2001 situation, so the original ABS weights were retained for 2001. Third, the implications of changes in the age distribution of the population were examined, based on population projections to 2050. A ,pure' change in the age distribution was examined by keeping the aggregate population size fixed and changing only the relative frequencies in different age-gender groups. Finally, the effects of a policy change to benefit taper rates in Australia were compared for 2001 and 2050 population weights. It is suggested that this type of exercise provides an insight into the implications for government income tax revenue and social security expenditure of changes in the population, indicating likely pressures for policy changes. [source]