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Poverty maps at local level might be misleading when based on direct (or area-specific) estimators obtained from a survey that does not cover adequately all the local areas of interest. In this case, small area estimation procedures based on assuming common models for all the areas typically provide much more reliable poverty estimates. These models include area effects to account for the unexplained between-area heterogeneity. When poverty figures are sought at two different aggregation levels, domains and subdomains, it is reasonable to assume a twofold nested error model including random effects explaining the heterogeneity at the two levels of aggregation. The paper introduces the empirical best (EB) method for poverty mapping or, more generally, for estimation of additive parameters in small areas, under a twofold model. Under this model, analytical expressions for the EB estimators of poverty incidences and gaps in domains or subdomains are given. For more complex additive parameters, a Monte Carlo algorithm is used to approximate the EB estimators. The EB estimates obtained of the totals for all the subdomains in a given domain add up to the EB estimate of the domain total. We develop a bootstrap estimator of the mean-squared error of EB estimators and study the effect on the mean-squared error of a misspecification of the area effects. In simulations, we compare the estimators obtained under the twofold model with those obtained under models with only domain effects or only subdomain effects, when all subdomains are sampled or when there are unsampled subdomains. The methodology is applied to poverty mapping in counties of the Spanish region of Valencia by gender. Results show great variation in the poverty incidence and gap across the counties from this region, with more counties affected by extreme poverty when restricting ourselves to women. [ABSTRACT FROM AUTHOR]

We propose a procedure associated with the idea of the E-M algorithm for model selection in the presence of missing data. The idea extends the concept of parameters to include both the model and the parameters under the model, and thus allows the model to be part of the E-M iterations. We develop the procedure, known as the E-MS algorithm, under the assumption that the class of candidate models is finite. Some special cases of the procedure are considered, including E-MS with the generalized information criteria (GIC), and E-MS with the adaptive fence (AF; Jiang et al.). We prove numerical convergence of the E-MS algorithm as well as consistency in model selection of the limiting model of the E-MS convergence, for E-MS with GIC and E-MS with AF. We study the impact on model selection of different missing data mechanisms. Furthermore, we carry out extensive simulation studies on the finite-sample performance of the E-MS with comparisons to other procedures. The methodology is also illustrated on a real data analysis involving QTL mapping for an agricultural study on barley grains. Supplementary materials for this article are available online. [ABSTRACT FROM PUBLISHER]

Combining information from two or more independent surveys is a problem frequently encountered in survey sampling. We consider the case of two independent surveys, where a large sample from survey 1 collects only auxiliary information and a much smaller sample from survey 2 provides information on both the variables of interest and the auxiliary variables. We propose a model-assisted projection method of estimation based on a working model, but the reference distribution is design-based. We generate synthetic or proxy values of a variable of interest by first fitting the working model, relating the variable of interest to the auxiliary variables, to the data from survey 2 and then predicting the variable of interest associated with the auxiliary variables observed in survey 1. The projection estimator of a total is simply obtained from the survey 1 weights and associated synthetic values. We identify the conditions for the projection estimator to be asymptotically unbiased. Domain estimation using the projection method is also considered. Replication variance estimators are obtained by augmenting the synthetic data file for survey 1 with additional synthetic columns associated with the columns of replicate weights. Results from a simulation study are presented. [ABSTRACT FROM PUBLISHER]

This article presents a pseudo-empirical likelihood approach to inference for multiple-frame surveys. We establish a unified framework for point and interval estimation of finite population parameters, and show that inferences on the parameters of interest making effective use of different types of auxiliary population information can be conveniently carried out through the constrained maximization of the pseudo-empirical likelihood function. Confidence intervals are constructed using either the asymptotic χ2 distribution of an adjusted pseudo-empirical likelihood ratio statistic or a bootstrap calibration method. Simulation results based on Statistics Canada's Family Expenditure Survey data show that the proposed methods perform well in finite samples for both point and interval estimation. In particular, a multiplicity-based pseudo-empirical likelihood method is proposed. This method is easily used for multiple-frame surveys with more than two frames and does not require complete frame membership information. The proposed pseudo-empirical likelihood ratio confidence intervals have a clear advantage over the conventional normal approximation-based intervals in estimating population proportions of rare items, a scenario that often motivates the use of multiple-frame surveys. All related computational problems can be handled using existing algorithms for pseudo-empirical likelihood methods with single-frame surveys. [ABSTRACT FROM AUTHOR]

The authors propose to estimate nonlinear small area population parameters by using the empirical Bayes (best) method, based on a nested error model. They focus on poverty indicators as particular nonlinear parameters of interest, but the proposed methodology is applicable to general nonlinear parameters. They use a parametric bootstrap method to estimate the mean squared error of the empirical best estimators. They also study small sample properties of these estimators by model-based and design-based simulation studies. Results show large reductions in mean squared error relative to direct area-specific estimators and other estimators obtained by "simulated" censuses. The authors also apply the proposed method to estimate poverty incidences and poverty gaps in Spanish provinces by gender with mean squared errors estimated by the mentioned parametric bootstrap method. For the Spanish data, results show a significant reduction in coefficient of variation of the proposed empirical best estimators over direct estimators for practically all domains. [ABSTRACT FROM AUTHOR]

A stability indicating RP HPLC method has been developed for the determination of gemcitabine hydrochloride. Chromatography was carried out on an ODS C18 column (250×4.6 mm; 5μ) using a mixture of methanol and phosphate buffer (40: 60 v/v ) as the mobile phase at a flow rate of 1.0 mL/min. The detection of the drug was monitored at 270 nm. The retention time of the drug was found to be 2.31 min. The method produced linear responses in the concentration range of 10 to 60 μg/mL of gemcitabine HCl. The method was found to be reproducible for analysis of the drug in injectable dosage forms. The stability of the drug was assessed by forced degradation studies. [ABSTRACT FROM AUTHOR]

Variance estimation after imputation is an important practical problem in survey sampling. When deterministic imputation or stochastic imputation is used, we show that the variance of the imputed estimator can be consistently estimated by a unifying linearize and reverse approach. We provide some applications of the approach to regression imputation, fractional categorical imputation, multiple imputation and composite imputation. Results from a simulation study, under a factorial structure for the sampling, response and imputation mechanisms, show that the proposed linearization variance estimator performs well in terms of relative bias, assuming a missing at random response mechanism. [ABSTRACT FROM PUBLISHER]

L'estimation de petits domaines a reç cu considérablement d'attention ces dernières années en raison de la demande croissante de statistiques régionales. Les modèles au niveau des domaines et des unités ont déjà été étudiés dans la littérature et les meilleurs estimateurs linéaires sans biais empiriques (EBLUP) pour les petits domaines ont été obtenus. Quoique cette méthode classique est utile pour estimer les moyennes régionales de faç con efficace sous l'hypothèse de normalité, ses résultats sont grandement influencés par la présente de données aberrantes. Dans cet article, les auteurs étudient les propriétés de robustesse des estimateurs classiques et ils proposent une méthode robuste pour l'estimation de petits domaines qui diminue le poids associé aux observations influentes lors de l'estimation des paramètres du modèle. Afin d'estimer l'erreur quadratique moyenne des estimateurs robustes des moyennes régionales, une méthode d'auto-amorç cage paramétrique est utilisée. Cette méthode peut être utilisée aux modèles dont la structure de covariance est bloc diagonale. Des simulations sont faites pour étudier le comportement des estimateurs robustes proposés en présence de valeurs aberrantes et aussi pour les comparer aux estimateurs EBLUP. La performance de l'estimateur 'boostrap' de l'erreur quadratique moyenne est aussi étudiée dans cette étude de simulations. Cette méthode robuste est appliquée à l'estimation de la superficie des cultures pour les comtés de l'Iowa en se basant sur des entrevues au niveau des fermes et en utilisant les données provenant du satellite LANDSAT comme information auxiliaire. La revue canadienne de statistique 37: 381-399; 2009 © 2009 Société statistique du Canada [ABSTRACT FROM AUTHOR]

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 is drawn according to a specific sampling design , and auxiliary data are observed for the units . Given the first-phase sample , a second-phase sample is selected from according to a specified sampling design , and ( y, x) is observed for the units . In some cases, the population totals of some components of 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. [ABSTRACT FROM AUTHOR]

Previously, small area estimation under a nested error linear regression model was studied with area level covariates subject to measurement error. However, the information on observed covariates was not used in finding the Bayes predictor of a small area mean. In this paper, we first derive the fully efficient Bayes predictor by utilizing all the available data. We then estimate the regression and variance component parameters in the model to get an empirical Bayes (EB) predictor and show that the EB predictor is asymptotically optimal. In addition, we employ the jackknife method to obtain an estimator of mean squared prediction error (MSPE) of the EB predictor. Finally, we report the results of a simulation study on the performance of our EB predictor and associated jackknife MSPE estimators. Our results show that the proposed EB predictor can lead to significant gain in efficiency over the previously proposed EB predictor. [ABSTRACT FROM AUTHOR]

Multiple-frame surveys are commonly used to decrease costs of sampling or to reduce undercoverage that could occur if only one sampling frame were used. We describe potential uses and examples of multiple-frame surveys. We then derive optimal linear estimators and pseudo- maximum likelihood estimators for the population total when samples are taken independently from each frame using probability sampling designs. We explore the properties of these estimators theoretically and through a simulation study. We also derive variance estimators and discuss some practical problems that may be encountered in multiple-frame surveys. [ABSTRACT FROM AUTHOR]

DNA microarrays can provide insight into genetic changes that characterize different stages of a disease process. Accurate identification of these changes has significant therapeutic and diagnostic implications. Statistical analysis for multistage (multigroup) data is challenging, however. ANOVA-based extensions of two-sample Z-tests, a popular method for detecting differentially expressed genes in two groups, do not work well in multigroup settings. False detection rates are high because of variability of the ordinary least squares estimators and because of regression to the mean induced by correlated parameter estimates. We develop a Bayesian rescaled spike and slab hierarchical model specifically designed for the multigroup gene detection problem. Data preprocessing steps are introduced to deal with unique features of inicroarray data and to enhance selection performance, We show theoretically that spike and slab models naturally encourage sparse solutions through a process called selective shrinkage. This translates into oracle-like gene selection risk performance compared with ordinary least squares estimates. The methodology is illustrated on a large microarray repository of samples from different clinical stages of metastatic colon cancer. Through a functional analysis of selected genes, we show that spike and slab models identify important biological signals while minimizing biologically implausible false detections. [ABSTRACT FROM AUTHOR]

The article discusses a study on the estimation of domain totals and means under survey-weighted regression imputation for missing items. Two methods to inference are used such as design-based with uniform response within classes and model-assisted with negligible response and an imputation model. Linearization variance estimators are derived and variance estimators of the bias-adjusted estimators are obtained.

In this paper based on a basic area level model we obtain second-order accurate approximations to the mean squared error of model-based small area estimators, using the Fay & Herriot (1979) iterative method of estimating the model variance based on weighted residual sum of squares. We also obtain mean squared error estimators unbiased to second order. Based on simulations, we compare the finite-sample performance of our mean squared error estimators with those based on method-of-moments, maximum likelihood and residual maximum likelihood estimators of the model variance. Our results suggest that the Fay–Herriot method performs better, in terms of relative bias of mean squared error estimators, than the other methods across different combinations of number of areas, pattern of sampling variances and distribution of small area effects. We also derive a noninformative prior on the model parameters for which the posterior variance of a small area mean is second-order unbiased for the mean squared error. The posterior variance based on such a prior possesses both Bayesian and frequentist interpretations. [ABSTRACT FROM AUTHOR]

Generalized regression(GREG) uses auxiliary variables with known population totals to improve efficiency of estimators and to ensure consistency with the known totals. Variance estimation for the GREG estimator of a total under stratified multistage sampling is considered. Customary resampling methods(jackknife, balanced repeated replication and bootstrap) for estimating the variance of a GREG estimator require the inversion of a P × P matrix for each resample, where P is the number of auxiliary variables with known population totals. This could lead to illconditioned matrices for some of the resamples. We apply the estimating function(EF) resampling method of Hu and Kalbfleisch[Hu, F., Kalbfleisch, J. D.(2000). The estimating function bootstrap(with discussion). Can. J. Statist. 28:449–499] to obtain variance estimators, using jackknife resampling. This method avoids repeated inverses. We extend the results to cover parameters defined as solutions of census estimating equations. The proposed method can be implemented from micro data files containing the GREG weights and the associated EF jackknife weights. [ABSTRACT FROM AUTHOR]

Emploi de poids d'echantillonnage pour I'estimation des moyennes de petits domaines au moyen du meilleur prédicteur linéaire sans biais pseudo-empirique Les auteurs développent une méthode d' estimation pour petits domaines à partir de poids d' échantillonnage et d' un modèle de régression linéaire à erreurs emboǐtées. Ils proposent plus spéci-fiquement l' emploi du meilleur prédicteur linéaire sans biais pseudo-empirique (pseudo-MPLSB) pour l' estimation des moyennes de petits domaines. Parce qu' il s' appuie sur un modèle, l' estimateur en question gagne en précision sur l' ensemble des domaines. Comme il tient compte des poids d' échantillonnage, il est asymptotiquement convergent par rapport au plan d' échantillonnage. Lorsqu' agrégé à la population entiére, il coïncide en outre avec l' estimateur obtenu par la régression classique. Les auteurs montrent aussi comment approximer l' erreur quadratique moyenne associée au modèle et l' estimer presque sans biais. Its comparent enfin le nouvel estimateur au MPLSB et au pseudo-MPLSB de Prasad & Rao (1999) au moyen de données déjà analysées par Battese, Harter & Fuller (1988). [ABSTRACT FROM AUTHOR]

The article reports on a study that proposes a small area estimation using a hierarchical Bayes approach to area level unmatched sampling and linking models. They compare inferences under unmatched models with those derived under the usual matched sampling and linking models, and then apply the proposed method to Canadian census undercoverage estimation, developing a full hierarchical Bayes approach using Markov Chain Monte Carlo sampling methods. Their analysis, using data from the 1991 Canadian census, shows that the proposed model fits the data well.

The empirical likelihood method under stratified random sampling is used for making inferences on finite population parameters. Our results show that it can lead to efficient estimators by making effective use of auxiliary population information in the form of overall population totals or means ascertained from external sources. Empirical likelihood ratio confidence intervals for the population mean are also studied, and adjusted intervals with asymptotically correct coverage rates are obtained. [ABSTRACT FROM PUBLISHER]

Poststratified estimators are commonly used in sample surveys to improve the efficiency of estimators and to ensure calibration to known poststrata counts. Similarly, generalized regression estimators are used to handle two or more poststratifiers with known marginal counts. In addition, weighting adjustment within weighting classes is used to handle unit nonresponse, and imputation within imputation classes is used to handle item nonresponse. For the full response case, asymptotic consistency of the jackknife variance estimator under stratified multistage sampling is established using mild regularity conditions on "residuals" similar to those of Scott and Wu for ratio and regression estimation under simple random sampling. A jackknife linearization variance estimator, obtained by linearizing the jackknife variance estimator, is also given. For unit nonresponse, the general case of poststrata cutting across weighting classes is considered, and a jackknife variance estimator and the corresponding jackknife linearization variance estimator are obtained. For item nonresponse, weighted mean imputation and weighted hot deck stochastic imputation within imputation classes are studied. Jackknife variance estimators, based on "adjusted" imputed values, are proposed, and the corresponding jackknife linearization variance estimators are obtained. Asymptotic consistency of the jackknife variance estimator is established for both the unit and item nonresponse cases under mild conditions on "residuals," assuming uniform response within classes. Simulation results for the poststratified estimator under weighted mean imputation and weighted hot deck stochastic imputation are presented. [ABSTRACT FROM AUTHOR]

Un modèle impliquant des effets aléatoires autocorrélés et des erreurs d'échantillonnages est proposé pour l'estimation des petites surfaces, utilisant à la fois des séries chronologiques et des données transversales. Les erreurs d'échantillonnages sont présumées avoir une matrice connue de variance-covariance bloc diagonale. Ce modèle est une extension d'un modèle bien connu dû à Fay et Herriot (1979) pour données transversales. Un estimateur à deux niveaux pour la moyenne d'une petite surface pour la période en cours est obtenu sous les hypothèses du modèle proposé avec autocorrélation connue, en dérivant d'abord l'estimateur de la meilleure prédiction linéaire non biaisée (MPLNB), en assumant connues les variances et en les remplaçant par leurs estimateurs consistants. Généralisant l'approche de Prasad et Rao (1986, 1990) pour le modèle de Fay-Herriot, on a obtenu un estimateur de l'erreur quadratique moyenne (EQM) de l'estimateur à deux niveaux, qui est une bonne approximation d'ordre deux lorsque le nombre de points dans le temps, T, est petit ou modérément grand, et que le nombre de petites surfaces, m, est relativement grand. Le cas où l'autocorrélation est inconnue, est aussi considéré. Des résultats limités basés sur des études de simulations et portant sur l'efficacité des estimateurs à deux niveaux et la précision de l'EQM, sont présentés. [ABSTRACT FROM AUTHOR]

In a dual frame survey, samples are drawn independently from two overlapping frames that are assumed to cover the population of interest. This article considers the case when at least one of the samples is selected by a complex design involving, e.g., multistage sampling. A "pseudo"-maximum likelihood estimator of a population total or a mean for such dual frame surveys is proposed. An advantage of the proposed estimator is that the same weights are used for all the variables, unlike the estimators of Hartley and Fuller and Burmeister. Asymptotic properties of the estimator are studied, including its efficiency. An alternative "single frame" estimator, based on the design induced by the two separate designs, is also studied. Results of a limited simulation study indicate that our estimator is essentially as efficient as those of Hartley and Fuller and Burmeister and can lead to significant efficiency gains over the single frame estimator. [ABSTRACT FROM AUTHOR]

For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction achieved by the jackknife and balanced repeated-replication estimators of a nonlinear function of totals are also given. [ABSTRACT FROM AUTHOR]

Relative efficiency of estimators of the common mean of possibly different normal populations N(mu, sigma[sup 2, sub i]) is investigated empirically. A weighted least squares estimator mu[sub 3], with weights based on a modification of minimum norm quadratic unbiased (MINQU) estimators of the sigma[sup 2, sub i], is found to be substantially more efficient than the maximum likelihood (ML) estimator of mu when the heterogeneity in the sigma[sub i] is small to moderate and the number of sample observations from a population is small. The jackknife t statistic for mu[sub 3] performed well in regard to both coverage probability and expected length of the confidence interval. [ABSTRACT FROM AUTHOR]

The problem of estimating the variance of the ratio estimator in sampling with probability proportional to aggregate size is investigated. The form of nonnegative unbiased variance estimators is found. For sample size n = 2, it is shown that there is at most one nonnegative unbiased variance estimator, whereas for n > 2, two different, possibly nonnegative, unbiased variance estimators are proposed. The performance of the proposed unbiased variance estimators, as regards their stabilities and probabilities of getting a negative value, is empirically investigated employing a variety of real populations. [ABSTRACT FROM AUTHOR]

In this article, the operating characteristics of recently proposed tests for trend in correlated binary data arising in laboratory studies of developmental toxicity are examined using both computer-generated and experimental data. Specifically, we consider adjusted Cochran-Armitge tests based on the Rao-Scott transformation which are of the same general form as that for uncorrelated data. In addition, generalized score tests based on generalized estimating equations allowing for extrabinomial variation in the data are discussed. Specific forms of these statistics demonstrating favorable type I and type II error rates are identified and recommended for use in practice. The application of these tests is illustrated using data from studies of developmental toxicity that have been reported in the literature. [ABSTRACT FROM AUTHOR]

A new solution to the problem of variance estimation with one unit per stratum is presented. This method may lead to smaller bias in variance estimation, in many situations, than the methods of 'collapsed strata'. It requires that we can associate with the strata concomitant variables which are correlated with the strata means. Several numerical examples with one or two concomitant variables are considered. [ABSTRACT FROM AUTHOR]

Stabilities of estimators of the population total and stabilities of their variance estimators are compared for the following methods of sampling two units per stratum: (a) the I.P.P.S. (inclusion probabilities proportional to size) methods of Brewer, Fellegi and Hanurav using the Horritz-Thompson estimator, (b) Des Raj's and Murthy's methods of p.p.s, sampling without replacement, (c) the Rao-Hartley-Cochran method, (d) Lahiri's method using a ratio estimator and (e) p.p.s. sampling with replacement using the customary estimator. A wide variety of populations, natural as well as artificial, is used for this purpose. The empirical study is supplemented by a semitheoretical study based on an often-used super-population model. The two studies lead to the following major conclusions: (1) Murthy's method is preferable over the other methods when a stable estimator as well as a stable variance estimator are required. (2) The Rao-Hartley-Cochran variance estimator is the most stable, but their estimator might lead to significant losses in efficiency. (3) Hanurav's method does not lead to significant improvements over Fellegi's or Brewer's methods with regard to stability of the variance estimator. [ABSTRACT FROM AUTHOR]

A correction to the article "On measuring the variability of small area estimators under a basic area level model," that appeared in the 2005 issue is presented.

Two-phase sampling is useful when the sampling frame contains little or no useful auxiliary information on the population elements. To estimate a finite population total under a two-phase design, we consider two point estimators: (i) the double expansion estimator and (ii) the Hajèk estimator. For each estimator, we consider two competing unbiased variance estimators: (i) the Horvitz-Thompson (HT) type variance estimator and (ii) the Sen-Yates-Grundy (SYG) type variance estimator. In this paper, we make an empirical study of the properties of these variance estimators in terms of stability as well as the tendency for the HT-type variance estimator to take on negative values. We provide simulation results under a two-phase sampling design, based on simple random sampling in the first phase to observe a size variable and probability proportional-to- size sampling without replacement in the second phase. [ABSTRACT FROM AUTHOR]