Calibrated Maximum Likelihood Design Weights in Survey Sampling

• Activity Number: 477
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Sarjinder Singh*+ and Stephen A. Sedory
• Companies: Texas A&M University at Kingsville and Texas A&M University at Kingsville
• Keywords: Calibration of design weight ; estimation of population mean ; simulation study ; soultion to non-linear equations ; Maximum likelihood function ; maximum likelihood design weights

Abstract

In this paper, we propose a new technique to calibrate the design weights in survey sampling by the method of maximum likelihood. We show that the design weights used in the Narain (1951) and the Horvitz and Thompson (1952) estimators are in fact maximum likelihood design weights. Later, we discuss two different situations: ( a ) when the variance of the calibrated weights is assumed to be known; and ( b ) when the variance of the calibrated weights is assumed to be unknown. Under situation ( a ), we obtain the linear regression estimator as a special case of it, and under situation ( b ) we obtain a new estimator, slightly different than the linear regression estimator. The calibrated estimators available since Deville and Särndal (1992) belong to the former case ( a ) whereas case ( b ) is a new development in this area. A simulation study has been carried out to investigate the performance of the resultant estimators. At the end, an application based on a real dataset from the biosciences is given.