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.

中文翻译：

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基于重采样方法的复杂采样设计中的估计

通常，为了选择具有代表性的总体样本，我们使用多种概率抽样方法的组合，称为复杂抽样设计。复杂的抽样设计通常需要非常复杂的数学计算来提供总体参数的无偏估计。因此，在实践中通常只使用有限数量的抽样设计。在本研究中，为了克服这种复杂性，我们提出了一种基于重采样的通用估计方法，该方法适用于所有标准设计，无论是传统设计还是自适应设计。在这种方法中，我们将 Murthy 估计量计算为总体均值及其方差估计量的无偏估计量，而无需进行大量的数学计算。使用这种方法，研究人员可以在保证估计量无偏的情况下执行任何概率设计。为了展示这种能力并作为该方法的应用，我们引入了自适应随机游走采样作为一种复杂而有效的采样设计，适用于基于样方的环境群体。尽管这种设计很复杂，但本文提出的方法为基于设计的总体均值提供了无偏估计，然后使其成为实用的设计。模拟证实了该方法的预期性能。本文提出的方法基于设计为总体均值提供了无偏估计，然后使其成为实用的设计。模拟证实了该方法的预期性能。本文提出的方法基于设计为总体均值提供了无偏估计，然后使其成为实用的设计。模拟证实了该方法的预期性能。