Unconditional Variance Estimation Under Complex Surveys

Summary The unconditional framework treats the samples and the variables of interest as random variables. This is particularly suitable with analytic inference, when modelling survey data. We show that variance estimation does not involve finite population corrections and joint‐inclusion probabilities, even with large sampling fractions and under sampling without‐replacement. The main advantage of the variance estimator is its simplicity. We show that it is asymptotically unbiased, under unequal probability designs incorporating stratification, multistage and informative sampling. We consider a general class of parameters defined by estimating equations, such as means, ratios, quantiles and parameters of generalised linear models. We also show how auxiliary information can be incorporated. A test statistic is derived for hypotheses on parameters. We propose a consistent variance estimator under ordered systematic sampling.