Adaptive inference for multi-stage unbalanced exponential survey data

Two-stage sampling usually leads to higher variances for estimators of means andregression coecients, because of intra-cluster homogeneity. One way of allowing forclustering in tting a linear regression model is to use a linear mixed model with twolevels. If the estimated intra-cluster correlation is close to zero, it may be acceptableto ignore clustering and use a single level model. In this paper, an adaptive strategy isevaluated for estimating the variances of estimated regression coecients. The strategyis based on testing the null hypothesis that random eect variance component is zero. Ifthis hypothesis is accepted the estimated variances of estimated regression coecientsare extracted from the one-level linear model. Otherwise, the estimated variance isbased on the linear mixed model, or, alternatively the Huber-White robust varianceestimator is used. A simulation study is used to show that the adaptive approachprovides reasonably correct inference in a simple case.