抽样调查和蒙特卡洛方法中的随机比较

本项目拟研究随机比较理论与抽样调查理论的交叉问题，主要是使用随机序来研究各种抽样方法的随机比较问题。通过将随机序引入抽样调查理论，使得抽样误差的比较不再局限于均值和方差，可以采用更一般的损失函数形式（比如凸函数），设法建立更为精细和深层次的结果。我们将在有限总体下，考虑连续抽样、拒绝抽样和多项抽样等几种不等概率抽样方法，研究它们的随机比较性质，并进一步探索随机序在Monte Carlo 随机法中的应用。同时，我们还将研究与项目相关的多维随机序的微观层面性质，以便完善项目涉及的随机序方法和理论。拟通过本项目的研究，更加细致地刻画各种抽样方法的概率性质，以期对各种抽样方法的性质有更深层次的理解，进而为抽样理论和抽样实践提供更好的支持和指导。

This project intends to investigate the intersecting problem of stochastic comparison and sampling survey theory, and mainly to discuss the stochastic comparisons of various sampling methods by using the stochastic orders.By introducing stochastic orders to sampling survey theory, the comparisons of sampling error are no longer limited to the mean and variance, and can be used in a more general form of loss function (such as convex function) to establish more detailed and deep results.We will consider several unequal probability sampling methods under the finite population, such as successive sampling, rejective sampling and multi-nomial sampling, etc, study their stochastic comparison properties, and further explore the applications of stochastic orders in Monte Carlo stochastic method. Meanwhile, we will also study micro-level properties of multidimensional stochastic orders related to the project in order to improve the stochastic ordering method and theory the project involved.Through the research of this project, we expect to depicte the probability properties of various sampling methods more carefully in order to understand the properties of various sampling methods more deeply, and thus to provide better support and guidance for the sampling theory and practice.