Approximate optimal allocation in repeated sampling from a finite population

Samples of size n are drawn from a finite population on each of two occasions. On the first occasion a variate x is measured, and on the second a variate y. In estimating the population mean of y, the variance of the best linear unbiased combination of means for matched and unmatched samples is itself minimized, with respect to the sampling design on the second occasion, by a certain degree of matching. This optimal allocation depends on the population correlation coefficient, which previous authors have assumed known. We estimate the correlation from an initial matched sample, then an approximately optimal allocation is completed and an estimator formed which, under a bivariate normal superpopulation model, has model expected mean square error equal, apart from an error of order n^-2, to the minimum enjoyed by any linear, unbiased estimator.     

Estimating the Size of a Subdomain: An Application in Auditing

This article suggests an alternative to the ratio estimator for estimating the total size of a subdomain of a population. The application that served as the genesis for this work is from auditing. The problem is to estimate the total of sales transactions that are not tax exempt from an audit sample of the population of nontaxed sales transactions. A superpopulation approach, which models the unit's probability of belonging to the subdomain as a function of its size, leads to a family of estimators. The simplest member of this famiiy is one in which that function is specified to be a constant. The optimal estimator for this model performs markedly better than the ratio estimator when the assumption is true and often performs better when it is not, though in that case it is biased. Stratification is shown to reduce this bias and at the same time make the ratio estimator more similar to the optimal estimator. A simulation experiment shows that the theoretical advantages hold in a real audit population.     

Model and design correspondence in finite population sampling

A correspondence rule is suggested for the choice of a sampling design when prior knowledge concerning a finite population is available. Designs satisfying the correspondence rule are discussed in the case of random permutations models. A general optimality theorem is given for strategies under such models. Approximate correspondences satisfied by systematic sampling and πps sampling are also indicated.     

On the Use of Superpopulation Model in Estimation of Population Mean in Two-Occasion Rotation Patterns

The present work is an attempt to study the estimation of the population mean on the current occasion in two-occasion successive (rotation) sampling under a superpopulation model. Six different estimators are proposed for estimating the current population mean in two-occasion successive (rotation) sampling. Optimum replacement policies and performances of the proposed estimators have been discussed. Results are interpreted via empirical studies.     

Estimation of Laspeyres Price Indexes Using the Prediction Approach for Finite Population Sampling

Estimators of chain and fixed-base Laspeyres price indexes are studied using the prediction approach to finite population sampling. The estimators include some that are based on those used in several U.S. government index programs and others derived from prediction models. Biases and variances of the estimators are studied for a case in which the reference period index weights are unknown for nonsample items. Under a model for a one-period price change in which items have common within-stratum means, unbiased estimators can be constructed, but under a more general regression model, special sample balance conditions are needed for unbiasedness of those estimators. The theory for the estimators of fixed-base indexes is illustrated in an empirical study using a population of items priced for the U.S. Consumer Price Index.     

Resolving the Mixed Models Controversy

Two standard mixed models with interactions are discussed. When each is viewed in the context of superpopulation models, the mixed models controversy is resolved. The tests suggested by the expected mean squares under the constrained-parameters model are correct for testing the main effects and interactions under both the unconstrained-and constrained-parameters models.     

Bayes and minimax estimators for two-stage sampling from a finite population under measurement error models

We consider Bayes and Minimax estimates of population mean in sampling from a finite population in two-stages using simple random sampling without replacement at each stage, when the true values of the characteristic cannot be observed but only the values mixed with some measurement errors are observed. Minimax values of sample sizes have been found in case of equal-sized clusters and equal-sized second stage samples.     

A confidence interval for the median of a finite population under unequal probability sampling: A model-assisted approach

This paper presents a method for constructing confidence intervals for the median of a finite population under unequal probability sampling. The model-assisted approach makes use of the _L1$L_1$-norm to motivate the estimating function which is then used to develop a unified approach to inference which includes not only confidence intervals but hypothesis tests and point estimates. The approach relies on large sample theory to construct the confidence intervals. In cases when second-order inclusion probabilities are not available or easy to compute, the Hartley–Rao variance approximation is employed. Simulations show that the confidence intervals achieve the appropriate confidence level, whether or not the Hartley–Rao variance is employed.     

ESTIMATION PROCEDURES FOR CATEGORICAL SURVEY DATA WITH NONIGNORABLE NONRESPONSE

We consider surveys with one or more callbacks and use a series of logistic regressions to model the probabilities of nonresponse at first contact and subsequent callbacks. These probabilities are allowed to depend on covariates as well as the categorical variable of interest and so the nonresponse mechanism is nonignorable. Explicit formulae for the score functions and information matrices are given for some important special cases to facilitate implementation of the method of scoring for obtaining maximum likelihood estimates of the model parameters. For estimating finite population quantities, we suggest the imputation and prediction approaches as alternatives to weighting adjustment. Simulation results suggest that the proposed methods work well in reducing the bias due to nonresponse. In our study, the imputation and prediction approaches perform better than weighting adjustment and they continue to perform quite well in simulations involving misspecified response models.     

Admissibility of Linear Predictors in the Superpopulation Model with Respect to Inequality Constraints under Matrix Loss Function

Admissibility of linear predictors for the linear quantity Qy is investigated in a superpopulation model with respect to some inequality constraints. Necessary and sufficient conditions for a linear predictor to be admissible in the class of homogeneous linear predictors and the class of inhomogeneous linear predictors are obtained, respectively, under matrix loss function.