Sparse and efficient replication variance estimation for complex surveys

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Jae Kwang Kim and Changbao Wu¹

Abstract

It is routine practice for survey organizations to provide replication weights as part of survey data files. These replication weights are meant to produce valid and efficient variance estimates for a variety of estimators in a simple and systematic manner. Most existing methods for constructing replication weights, however, are only valid for specific sampling designs and typically require a very large number of replicates. In this paper we first show how to produce replication weights based on the method outlined in Fay (1984) such that the resulting replication variance estimator is algebraically equivalent to the fully efficient linearization variance estimator for any given sampling design. We then propose a novel weight-calibration method to simultaneously achieve efficiency and sparsity in the sense that a small number of sets of replication weights can produce valid and efficient replication variance estimators for key population parameters. Our proposed method can be used in conjunction with existing resampling techniques for large-scale complex surveys. Validity of the proposed methods and extensions to some balanced sampling designs are also discussed. Simulation results showed that our proposed variance estimators perform very well in tracking coverage probabilities of confidence intervals. Our proposed strategies will likely have impact on how public-use survey data files are produced and how these data sets are analyzed.

Key Words

Bootstrap; Calibration; Jackknife; Linearization method; Replication weights; Sampling design; Spectral decomposition.

Table of content

1 Introduction

2 A general procedure for constructing fully efficient replication weights

3 Sparse and efficient replication weights

4 Validity

5 Extension to some balanced sampling designs

6 Simulation study

7 Some concluding remarks

 

 

 

 

 

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¹    Jae Kwang Kim, Department of Statistics, Iowa State University, Ames IA 50011-1210. E-mail: jkim@iastate.edu; Changbao Wu, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo ON N2L 3G1. E-mail: cbwu@uwaterloo.ca.