THREE-STAGE POINT ESTIMATION OF THE MEAN IN POSTSTRATIFICATION

ABSTRACT

Poststratification is often used in sample survey when the identification of stratum cannot be achieved in advance. Suppose that a random sample of size n is collected from a population, and one wishes to estimate the mean of the population by the poststratification estimator subject to the loss function measured by the sum of squared error due to estimation and cost of observations. When the variance of each stratum is unknown, the optimal fixed sample size for minimizing the risk cannot be used. We therefore apply Hall's three-stage procedure to the problem and study its asymptotic properties of the moments and the risk.

Keywords:

• Minimum risk approach
• Poststratification
• Stopping time
• Three-stage procedure
• Uniform integrability

ACKNOWLEDGMENTS

The author is grateful for the suggestions and comments made by the referee and an Associate Editor. This research was partially supported by National Science Council of the Republic of China.