  Model-assisted estimation with complex survey data is an important practical
problem in survey sampling. When there are many auxiliary variables, selecting
significant variables associated with the study variable would be necessary to
achieve efficient estimation of population parameters of interest. In this
paper, we formulate a regularized regression estimator in the framework of
Bayesian inference using the penalty function as the shrinkage prior for model
selection. The proposed Bayesian approach enables us to get not only efficient
point estimates but also reasonable credible intervals. Results from two
limited simulation studies are presented to facilitate comparison with existing
frequentist methods.
