Research On The Improvement Of Stratified Sampling Method Based On Spatial Clustering

As a non-comprehensive survey,sampling survey plays an important role in sample statistics.It is widely used in various fields such as resources,environment,economy and society in that it is economical,timely and accurate.Among them,stratified sampling is a more widely used sampling method,which divides the population into several subpopulations through a certain principle to reduce the size of the population and the number of samples,thereby improving the estimation accuracy and sampling efficiency.However,traditional stratified sampling faces two problems:(1)The traditional stratification method is mostly based on certain characteristics of the sampling unit,and cannot consider the spatial correlation between the sample units;(2)After stratification,probability sampling is usually used to distribute the sample size according to a certain ratio,and simple random sampling is performed at each layer,ignoring the influence of the unit size of each layer.Spatial clustering and unequal sampling provide ideas for improving the traditional stratified sampling.This paper introduces the spatial clustering algorithm in machine learning and ?PS sampling in unequal probability sampling,combines stratified sampling with spatial clustering and?PS sampling,and proposes a stratified sampling method based on spatial clustering and unequal probability which is applied to the hotel industry in Shanxi Province to conduct a sampling empirical study to verify the effectiveness of this sampling method.Based on this,the main works of this paper are as follows:(1)Three spatial clustering methods: K-means spatial clustering,DBSCAN spatial clustering and spectral clustering are used.The spatial information of the research object and its own attribute information are considered to determine the clustering factors.Spatial weight matrix was constructed based on longitude and latitude coordinates to test the spatial autocorrelation of clustering factors.Then,the spatial clustering result is used to stratify the research objects,and the spatial correlation among sample units is considered.(2)Two-stage sampling with unequal probabilistic and without replacement based on the ?PS sampling is proposed.The first stage uses the scale of each layer after stratification as an auxiliary variable to implement ?PS sampling which is strict.The second stage uses simple random sampling to draw samples,considering the impact of each strata unit on the sampling.(3)Shanxi province hotel data is crawled from the Meituan website for empirical research,estimating the average hotel rating,and determining eight clustering factors including the hotel's longitude,latitude,distance from the station,distance from the commercial center,lowest price,number of reviews,number of competing hotels and their average lowest price.The spatial autocorrelation test results show that the clustering factor rejects the null hypothesis at a significance level of 1%,and further spatial analysis can be carried out.The hotel spatial clustering results can be combined with factors such as the hotel's geographic location,local economic development and consumption level to analyze the rationality of the clustering results.Compared with traditional simple random sampling and unequal stratified sampling based on administrative divisions,the unequal stratified sampling method based on spatial clustering shows higher estimation accuracy and sampling efficiency.The unequal stratified sampling method based on spatial clustering proposed in this paper considers the spatial correlation between sample units and the influence of the size of each layer of the unit,solves the current problems faced by traditional stratified sampling,and provides new stratification ideas and sampling methods.