【作者】 张涛；

【导师】 米子川；

【作者基本信息】 山西财经大学 ， 统计学， 2021， 硕士

【摘要】 抽样调查作为一种非全面的调查,在样本统计方面发挥着重要作用,凭借其经济性、时效性和准确性的特征广泛应用于资源、环境、经济和社会等各个领域当中。其中,分层抽样是应用较为广泛的抽样方法,通过某种原则将总体划分成若干个子总体,达到缩小总体规模和需要抽取的样本量的目的,从而能够提高估计精度,提升抽样效率。但是传统分层抽样面临两个问题:(1)传统分层方法多是按抽样单元的某种特征进行分层,无法考虑到样本单元之间的空间相关性;(2)分层后,通常是使用概率抽样,按某一比例对样本量进行分配,在每层进行简单随机抽样,忽略了各层单元规模的影响。空间聚类和不等概抽样为改进传统分层抽样提供了思路,本文引入机器学习中的空间聚类算法和不等概抽样中的πPS抽样,将分层抽样与空间聚类、πPS抽样相结合,提出基于空间聚类的不等概分层抽样方法,并应用于山西省酒店行业进行抽样实证研究,验证这种抽样方法的有效性。基于此,本文的主要工作如下:(1)引入K-means空间聚类、DBSCAN空间聚类和谱聚类三种空间聚类方法,综合考虑研究对象的空间信息和自身属性信息确定聚类因子,利用基于经纬度坐标构建的空间权重矩阵对聚类因子进行空间自相关性检验,进而利用空间聚类结果对研究对象进行分层,考虑了样本单元之间的空间相关性。(2)提出基于πPS抽样的两阶段不放回不等概抽样,第一阶段利用分层后各层单元规模作为辅助变量实施严格的n(28)2的πPS抽样,第二阶段通过简单随机抽样抽取样本,考虑了各层单元规模对抽样的影响。(3)从美团网站爬取山西省酒店数据用于实证研究,对酒店评分均值进行估计,确定了酒店经度、纬度、相距车站距离、相距商业中心距离、最低价、评论条数、竞争酒店数量以及竞争酒店平均最低价8个聚类因子,空间自相关性检验结果显示,聚类因子在1%的显著性水平下拒绝原假设,可以进一步进行空间分析。将酒店空间聚类结果与酒店地理位置及所属地区经济发展、消费水平等因素相结合,分析聚类结果的合理性。与传统简单随机抽样和基于行政区划分的不等概分层抽样相比,基于空间聚类的不等概分层抽样方法表现出更高的估计精度和抽样效率。本文提出的基于空间聚类的不等概分层抽样方法考虑了样本单元之间的空间相关性和各层单元规模的影响,解决了目前传统分层抽样所面临的问题,提供了一种新的分层思路和抽样方法。更多还原

【Abstract】 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 πPS sampling in unequal probability sampling,combines stratified sampling with spatial clustering andπPS 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 πPS sampling is proposed.The first stage uses the scale of each layer after stratification as an auxiliary variable to implement πPS 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.更多还原