Conservative variance estimation for sampling designs with zero pairwise inclusion probabilities

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Peter M. Aronow and Cyrus Samii¹

Abstract

We consider conservative variance estimation for the Horvitz-Thompson estimator of a population total in sampling designs with zero pairwise inclusion probabilities, known as "non-measurable" designs. We decompose the standard Horvitz-Thompson variance estimator under such designs and characterize the bias precisely. We develop a bias correction that is guaranteed to be weakly conservative (nonnegatively biased) regardless of the nature of the non-measurability. The analysis sheds light on conditions under which the standard Horvitz-Thompson variance estimator performs well despite non-measurability and where the conservative bias correction may outperform commonly-used approximations.

Key Words

Horvitz-Thompson estimation; Non-measurable designs; Variance estimation.

Table of content

1 Introduction

2 Variance estimation for the Horvitz-Thompson estimator

3 Conservative bias correction for the Horvitz-Thompson variance estimator under non-measurability

4 Applications

5 Conclusion

 

 

 

 

 

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