New Stratification and Allocation Procedure for Stratified Simple Random Sampling Without Replacement, with Application to Business Surveys

• Activity Number: 507 - Business, Time Series, and Spatial Analysis Methods
• Type: Contributed
• Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Isolated Statisticians
• Author(s): Naomi Baum* and Danny Pfeffermann
• Companies: Israel Central Bureau of Statistics and Israel Central Bureau of Statistics, Hebrew University of Jerusalem, Univ. of Southampton
• Keywords: equal-strata-total stratification; geometric stratification; Neyman allocation; proportional allocation

Abstract

The number of strata, their boundaries, the total sample size and the allocated number of sample units to each stratum, all affect the magnitude of the standard error of estimators of totals. The total sample size is usually given, since it is determined by the available budget. This paper considers stratified, simple random sampling without replacement, when there are lower bounds to the sampling probabilities and to the number of allocated units per stratum, but the number of strata may vary. We propose to create as many strata as possible. A new procedure for an appropriate sampling design satisfying the bounds conditions is proposed. By this procedure, the sampling frame is divided into three sub-frames of large, medium and small size units. Next, the medium size sub-frame is stratified using the equal-strata-total stratification method and the small size sub-frame is stratified using the equal-size method, in both cases into as many strata as possible. The large units are all sampled. An allocation which under a commonly used assumption coincides with Neyman's allocation is applied for the medium size sub-frame, and proportional allocation is used for the small size sub-frame.