The Study Of Generalized Balanced Sampling And Its Model-assisted Estimation Method

In most of the current sampling surveys in China,the balanced sampling method is rarely used in the sampling design.In the information age,it is easier to obtain auxiliary information.It is convenient to use the balanced sampling method to obtain more representative samples which play a key role in improving the accuracy of sampling estimation.When the relationship between the auxiliary variable and interest variable is linear,the traditional balanced sample has a strong representativeness,and the Horvitz-Thompson estimator is better under the balanced sample.In actual sampling,there is a case that the superpopulation model is a non-linear regression model or its form is unknown.When the balanced variables are completely known for all units of population,this paper improves the traditional balanced sampling condition,proposes a more adaptable generalized balanced sampling.When the balanced variables are unknown for all units of population,if we implement balanced sampling by the known auxiliary variables,the sample taken is not representative of the population.This paper proposes a sampling design combining balanced sampling with double sampling.In the double sampling,the necessary auxiliary variable information is obtained firstly,and the generalized balanced sampling is carried out secondly.In both cases,the generalized balanced sampling improves the representativeness of the final sample.Because the conditions of balanced sampling are not fully satisfied,this paper uses the idea of generalized regression estimator to adjust the traditional balanced Horvitz-Thompson estimator and proposes generalized balanced regression estimator in the sampling estimation stage.In both cases,compared with the traditional estimator,the generalized balanced regression estimator has higher accuracy and more stable variance.Besides,the estimator is asymptotically design unbiased and consistent.This paper applies the generalized balanced sampling and its generalized balanced regression estimator to household survey in China,and puts forward the idea of sampling design.In addition,the simulation and empirical analysis results show the superiority of the generalized balanced sampling and the generalized balanced regression estimator,when there is a close correlation between the balance variable and the interest variable.