On the Use of Auxiliary Data in Poisson Sampling

• Activity Number: 75
• Type: Contributed
• Date/Time: Monday, August 12, 2002 : 8:30 AM to 10:20 AM
• Sponsor: General Methodology
• Author(s): John Slanta*+ and Michel Hidiroglou
• Affiliation(s): U.S. Census Bureau and Statistics Canada
• Keywords: Poisson sampling ; Horvitz-Thompson estimator ; Hájek estimator ; Brewer estimator

Abstract

Sampling units independently at each draw from a frame can be achieved using Bernoulli or Poisson sampling. The use of Bernoulli sampling implies that the probability of selection is constant for each draw, whereas Poisson sampling implies that the probability of selection differs at every draw, normally being proportional to the size measure of the unit being selected. Estimators and associated variances can be of a Horvitz-Thompson type. However, auxiliary data in the form of population counts or x-variables can be used to advantage to improve the efficiency of the estimator. In the case of Bernoulli sampling, it is well known that the Hájek estimator will always have a variance that is lower than the one corresponding to the Horvitz-Thompson estimator. However, this is not always the case with Poisson sampling. In this paper, we provide conditions that determine as to which estimator has the smaller population variance. We also study the properties of the Brewer estimator and the optimal regression estimator. These estimators and their associated variances are numerically compared using data from the Industrial Research and Development Survey.