Optimal AK Composite Estimators for the Current Population Survey

• Activity Number: 512
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Zhou Yu*+ and Jun Shao and Yang Cheng
• Companies: U.S. Census Bureau/University of Wisconsin-Madison and University of Wisconsin-Madison and U.S. Census Bureau
• Keywords: Composite Estimator ; Current Population Survey ; Mean Square Error ; Quadratic form ; Sample notation

Abstract

The Current Population Survey (CPS) is a monthly household sample survey consisting of eight rotation groups so that each selected household will be interviewed for 4 consecutive months and another 4 consecutive months after resting 8 consecutive months. A composite type estimator is adopted in the CPS for the estimation of the monthly population total, which combines sample information from the current month survey and previous months using the fact that 75% households have data for two consecutive months. There are two tuning parameters, A and K, in the composite estimator to decide how to combine the available information, and thus this estimator is called the AK composite estimator. However, the current choices of the tuning parameter values were determined by some empirical studies without theory support. In this paper, we derive a formula of the mean squared error of the AK composite estimator, and show that this formula is a quadratic form of A for each fixed K. Using this result, we propose an easy-to-use method of choosing the tuning parameters A and K. Our method is data-driven, i.e., we propose a method to estimate some population quantities in the mean squared error formula using observed data.