关键词: 广义逆抽样, 模型辅助, 抽样估计, 虚拟变量, Murthy估计量

Abstract: The conventional probability sampling method can better ensure the randomness of sampling, but when sampling the population containing rare units, it cannot effectively guarantee the sampling quantity of rare units due to the randomness of sampling, which in turn affects the subsequent statistical inference. The inverse sampling method provides a new idea for this problem, especially the general inverse sampling is improved on the basis of the traditional inverse sampling design, which has more practical application value. Based on the general inverse sampling design method, this paper constructs a generalized regression estimator from the perspective of model-assisted estimation, further considers the data characteristics of the population, and reflects the characteristic difference between rare units and non-rare units in the super-population regression in the form of dummy variables. In the model, generalized regression estimators are constructed that take into account dummy variables. Through numerical simulation, the comparison shows that the estimation accuracy of the generalized regression estimator is improved a little compared with the design-based Murthy estimator, and the generalized regression estimator considering dummy variables proposed in this paper has a greater improvement. In this paper, the above theory is applied to the survey of Chinese enterprises, and the advantages of the two model-assisted estimators are confirmed by the actual enterprise data. In view of the fact that economic and social research objects are often more complex, in the follow-up to promote the use of the improved inverse sampling design and its estimation method for survey research, it is necessary to conduct more in-depth research on its design and estimation method to enhance the effectiveness and breadth of its practical application.

Key words: General Inverse Sampling, Model-assisted, Sampling Estimate, Dummy Variables, Murthy Estimator