Research On MPPS Balanced Sampling And Its Application

Multipurpose survey refers to estimating multiple indicators of the population by using samples obtained from one sampling.Because it reflects many aspects of social and economic phenomena,and has high operation economy and timeliness,multipurpose survey is widely used in government statistical survey.However,as China’s economic development enters the new normal,the population changes are becoming more frequent,the indicators are more diverse and the structure is more complex.For example,in the transformation from traditional mode to large-scale and modernized mode,Chinese agriculture presents new characteristics such as rural land transfer,new agricultural management entities,new varieties of crops,agricultural scale and industrialization.Facing the increasing demand for statistical data from the government and society,the shortcomings of current national statistical survey methods are becoming increasingly prominent.First,PPS sampling(sampling with probability proportional to size)and HT estimator(Horvitz-Thompson estimator)are commonly used sampling techniques.The inclusion probability of a unit is determined by its size variable.There are multiple size variables in multipurpose survey,and the inclusion probability is determined by the sum of size variables.When the distribution difference of these size variables is large,the inclusion probability is no longer strictly proportional to any size variable,resulting in unreasonable sampling weight of HT estimator and decreased estimation accuracy.Second,the current survey methods can not make full use of the information of multiple size variables,resulting in large differences between sample structure and population structure.How to effectively carry out multipurpose survey and ensure the representativeness of samples is an important problem to be solved by both statistical theorists and practical departments.In order to make rational use of multiple size variables to improve sample representativeness,MPPS sampling(sampling with multivariate probability proportional to size)and balanced sampling have attracted great attention.The two sampling methods use size variables in different ways.The inclusion probability of MPPS sampling is determined jointly by all the size variables.The unit with any large size variable has a high inclusion probability,and the unit with small size variables has a low inclusion probability.Compared with PPS sampling,the advantages of MPPS sampling are mainly reflected in two aspects.First,a unit with a large size variable and a small size variable has a larger inclusion probability.second,when the mean difference of size variables is large,the inclusion probability of the unit is not excessively dependent on the size variable with the largest mean.In the balanced sampling,the sample size variable satisfies the equilibrium equation,which effectively eliminates samples with large differences from the population structure and improves sample representativeness.At present,scholars have carried out a series of fruitful research work on MPPS sampling and balanced sampling.The two sampling methods are also applied to foreign government statistical surveys,such as the American agricultural survey and the French labor force survey.But there are two problems.First,in MPPS sampling,the inclusion probability of units is not strictly proportional to the size variable,and the HT estimator has a large sampling error.The existing literature mainly focuses on the selection and optimization of of estimators,and lacks the improvement of the sample selection process.Second,balanced sampling mainly adopts equal probability sampling or unequal probability sampling proportional to a certain size variable.When the inclusion probability is not strictly proportional to the size variable,the estimation accuracy of survey variables will also be reduced.There is little discussion on the inclusion probability of balanced sampling in the existing literature.Based on the detailed comparison between MPPS sampling and balanced sampling,this paper proposes a MPPS balanced sampling combining the two sampling methods.The new method uses all size variables to determine inclusion probability and extract samples to improve sample representativeness.Based on the beneficial practices and experience of government statistical surveys of the United States,Canada and the European Union,this paper applies MPPS balanced sampling to stratified sampling and two-stage sampling,which are common forms of large-scale social economic survey,and proposes stratified MPPS balanced sampling and two-stage MPPS balanced sampling.The implementation process of sampling method,approximate variance and variance estimation of HT estimator or generalized regression estimator are given.Based on genetic algorithm and mathematical programming method,stratification method and sample size determination in stratified MPPS balanced sampling are solved.Monte Carlo simulation is used to demonstrate the advantages of the new sampling method.Under the background of the rural revitalization strategy,improving China’s agricultural survey methods and providing comprehensive and accurate production data of various agricultural products are crucial to ensuring national food security and coordinating the regulation of important agricultural products.Taking China’s agricultural survey as an example,this paper deeply analyzes the shortcomings of the current survey methods,adopts the proposed methods to solve the multipurpose problems of major livestock and poultry surveys,remote sensing measurement of crop area and ground sampling survey,demonstrates the specific application steps,and demonstrates the applicability and operability of the proposed method.The research can not only provide replicable experience for the sampling scheme design of agricultural survey,but also provide a new choice for the sampling scheme design of population survey or economic survey.