Estimation in Complex Sampling Designs Based on Resampling Methods

Abstract

Generally, to select a representative sample of the population, we use a combination of several probabilistic sampling methods which is called a complex sampling design. A complex sampling design usually needs very sophisticated mathematical calculations to provide unbiased estimators of the population parameters. Therefore, only a limited number of sampling designs are commonly used in practice. In the present study, to overcome this complexity, we propose a general method of estimation based on resampling that is suitable for all standard designs, either conventional or adaptive. In this method, we calculate Murthy estimator as an unbiased estimator for the population mean and its variance estimator without intensive mathematical calculations. Using this method, researchers can perform any probability design with the guarantee that the estimator is unbiased. To show this ability and as an application of the method, we introduce Adaptive Random Walk Sampling as a complex and efficient sampling design, proper for the quadrat-based environmental population. Despite the complexity of this design, the method proposed in this paper provides unbiased estimator for the population mean based on the design and then makes it a practical design. Simulations confirm the expected performance of the method.