Jean-Claude Deville

Calibration Estimators in Survey Sampling

Abstract This article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information. Estimation is equivalent to attaching weights to the survey data. We focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations. We briefly mention an application to the case in which the information consists of known marginal counts in a two- or multi-way table, known as generalized raking. The general regression estimator (GREG) was conceived with multivariate auxiliary information in mind. Ordinarily, this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x. But we note that the GREG can be derived by a different route by focusing instead on the weights. The ordinary sampling weights of the kth observation is 1/πk , where πk is the inclusion probabilit...

Generalized Raking Procedures in Survey Sampling

Abstract We propose the name generalized raking for the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table. Our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1/π k , where π k is the inclusion probability of element k. New weights are derived by minimizing the total distance between original weights and new weights. The article makes contributions in three areas: (1) statistical inference conditionally on estimated cell counts, (2) simple calculation of variance estimates for the generalized raking estimators, and (3) presen...

Estimating means and percentages in a complex sampling survey : Application to a French national survey on sexual behaviour (ACSF)

Two-phase stratification sampling with unequal selection probabilities is a relatively cost-efficient strategy to address problems on a nationwide basis and to perform comparative analyses of specific subgroups. This was the case with the ACSF survey. Specific procedures to estimate the variances of unbiased estimators in complex sampling designs are not included in standard statistical packages and no specialized software is available for two-phase sampling. A detailed synthesis of general basic rules for inference about a target population from a probability sample is first presented. We follow with a standard procedure to estimate means and percentages with their confidence intervals according to the design. Finally, numerical results are discussed.

Selection of several unequal probability samples from the same population

The well-known problem of unequal probability sampling of fixed size from a finite population can be generalised in a partitioning problem of a population into subsets, having unequal inlcusion probabilities in each subset. A simple algorithm that allows one to solve this problem is presented. The random partition of a population can be used to easily solve questions related to sample coordination in repeated sample surveys: the management of the overlap and the rotation. An application is developed where the maximal overlap of two samples selected with unequal probabilities is reached. Nevertheless, this method has an inconvenience: the samples must be selected at the same time. In order to overcome this difficulty, another method based on the multi-phase sampling method is also proposed.