An "approximately unbiased" estimator may be uniformly larger than an" overestimate"

• Activity Number: 422
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Robert Edson*+ and Gary M Shapiro
• Companies: U.S. Department of Veterans Affairs and Statistics Without Borders
• Keywords: collapsed stratum variance estimator ; primary sampling unit ; multi-stage sampling

Abstract

This paper considers the best form of the collapsed stratum variance estimator. If you select 1 primary sampling unit per stratum and collapse 2 strata (say, A and B) together for each group, the usual estimator (Hansen et al., 1953) assigns a weight to stratum A's estimate equal to twice the measure associated with stratum B divided by the sum of the measures for the 2 strata. This estimator is known to overestimate the variance. We developed an alternative estimator that is approximately unbiased and assigns a weight to stratum A (B) of the square root of the ratio of stratum B's (A's) measure to its measure. We expected it would be a better estimator as an "approximately unbiased" estimate might be expected to produce better results than one known to be an overestimate. However, this paper shows the approximately unbiased estimator never results in a lower variance estimate than the overestimating variance estimator. A general cautionary conclusion from these results is that an "approximately unbiased estimator" can be worse and actually larger than an "overestimate estimator".