Penalized balanced sampling

Abstract

SUMMARY Linear mixed models are flexible and extensible models that c over a wide range of statistical methods. They have found many uses in estimation for complex surveys, particularly in small area estimation and in extensions of generalized regression estimation. They have also been used as a means of relaxing constraints in calibration estimatio n. The purpose of this work is to consider methods by which linear mixed models may be used at the design stage of a survey. This paper reviews the ideas of balanced sampling and the cube algorithm, and proposes an implementation of the cube algorithm by which penalized balanced samples can be selected. Such samples have the property that Horvitz-Thompson estimators from penalized balanced samples behave like linear mixed model-assisted survey regression estimators from unbalanced samples. The methodology is evaluated by using nonparametric and temporal linear mixed models in simulation experiments, and by using a spatial linear mixed model in an artificial but realistic sampling application, motivated by a 1991‐1996 Environmental Protection Agency survey of lakes in the Northeastern states of the United States.