Biometrika centenary: sample surveys

Despite Karl Pearso's stated aim that the ‘evolutionist has to become in the widest sense of the words a registrar-general for all forms of life’, the papers published in Biometrika on sample surveys have been mainly theoretical and do not start to appear until the 1940s.There has been little work on sampling in the life sciences, with the exception of capture–recapture methods. The major areas have been in variable probability designs, the foundations of inference for finite populations, analytic surveys and the role of selection mechanisms in inference. In recent years the work on survey analysis has been the outcome of an interaction between sample selection mechanisms and mainstream theory, with interesting consequences for both areas

Edgeworth approximations to the distribution of the sample mean under simple random sampling.

We derive the Edgeworth expansion to order n-1 of the cumulative distribution function of the studentized sample mean under simple random sampling from a finite population

A constrained MINQU estimator of correlated response variance from unbalanced data in complex surveys.

This paper is concerned with the estimation of correlated response variance from unbalanced data in complex surveys. The Minimum Variance Quadratic Unbiased Estimator (MINQUE) proposed by Rao (1971, 1972) is often used for variance components estimations. However, for unbalanced data the equations for obtaining the MINQU estimates are very difficult to solve. In this paper we propose a constrained MINQU estimator by substituting robust unbiased estimates for the random residual errors in the MINQUE equations to obtain estimates of the correlated response variance. We demonstrate through numerical and empirical studies that the constrained MINQUE is efficient compared to the full MINQU estimator. We also point out that the constrained MINQU estimator can be used in other cases where reducing the complexity of the MINQUE equations is desired

Domains of study and poststratification

Sugden and Smith (2002. J. Statist. Plann. Inference 102, 25-38) investigated conditions under which exact linear unbiased estimators of linear estimands, and also exact quadratic unbiased estimators of quadratic estimands, could be constructed under the randomisation approach. In this paper the method is applied to domains of study and extended to poststratified estimators of finite population totals. The resulting estimators generalise some of those in Doss et al. (1979. J. Statist. Plann. Inference 3, 235-247). Some further properties of these estimators are explored

Exact linear unbiased estimation in survey sampling

The concept of the linearity of estimators in finite population inference is not well defined. We propose that linearity should be defined for both estimators and estimands and that strict linearity should be related constructively to the property of unbiasedness. We establish the conditions for the class of general linear estimators, introduced by Godambe (J. Roy. Statist. Soc. 17 (1955) 269), to be strictly linear. The ideas are extended to quadratic estimators of quadratic estimands. The implications are explored for ratio estimators, and domains of study, the latter extendible to poststratification

The time series analysis of compositional data

The analysis of repeated surveys can be approached using model-based inference, utilising the methods of time series analysis. On a long run of repeated surveys it should then be possible to enhance the estimation of a survey parameter. However, many repeated surveys that are suited to this approach consist of variables that are proportions, and hence are bounded between 0 and 1. Furthermore interest is often in a multinomial vector of these proportions, that are sum-constrained to 1, i.e., a composition. A solution to using time series techniques on such data is to apply an additive logistic transformation to the data and then to model the resulting series using vector ARMA models. Here the additive logistic transformation is discussed which requires that one variable be selected as a reference variable. Its application to compositional time series is developed, which includes the result that the choice of reference variable will not affect any final results in this context. The discussion also includes the production of forecasts and confidence regions for these forecasts. The method is illustrated by application to the Australian Labour Force Survey