基于潜变量模型的多元有序数据轮廓分析法  

The Profile Analysis of Multi-ordinal Data Based on Underlying Variable Model

作　　者：孙丰霖 鲁统宇 类淑河[3] SUN Feng-lin;LU Tong-yu;LEI Shu-he(College of Oceanic and Atmospheric Sciences,1.Ocean University of China,Qingdao 266100,China;School of Mathematical Sciences,1.Ocean University of China,Qingdao 266100,China;School of Economics and Management,China Jiliang University,Hangzhou 310018,China)

机构地区：[1]中国海洋大学海洋与大气学院,山东青岛266100 [2]中国计量大学经济与管理学院,浙江杭州310018 [3]中国海洋大学数学科学学院,山东青岛266100

出　　处：《统计与信息论坛》2019年第5期3-9,共7页Journal of Statistics and Information

基　　金：国家社会科学基金项目<大数据背景下定序数据的统计推断研究>(15BTJ016)

摘　　要：提出了一种适用于多元有序数据的轮廓分析方法。鉴于有序数据无法满足轮廓分析对数据正态性的要求,采用潜变量模型对有序变量进行赋值,利用Bootstrap方法重构样本,使重构后的新数据满足正态性且总体均值与原样本一致,因而可以将轮廓分析法应用于有序数据均值向量的比较问题。讨论了单样本情形的同水平假设、两样本和多样本情形的平行、同水平和平坦性假设,并给出相应的检验统计量和拒绝域。最后,通过随机模拟来检验该方法的合理性,并得到结论:样本质量较高时,该方法在控制第一类错误和提高检验的功效上效果很好;对于一般样本而言,该方法的实际第一类错误较名义值有所增大,可通过提高原始样本量、降低名义第一类错误和进行多次试验来解决。The method of profile analysis for multi-ordinal data is proposed in this paper.Because of the non-continuity,the multi-ordinal variables can not meet the requirement of profile analysis that the variables should obey multi-normal distribution,so we assign the variable according to the underlying variable model,resample the original data by bootstrap and retain the mean information into reconstructed sample obeying multi-normal distribution.The reconstructed sample has the same population mean vector with original data,and then we can use profile analysis to compare the mean vectors of the reconstructed sample include the level hypothesis for single sample,the parallelism hypothesis,the level hypothesis and the flatness hypothesis for two-sample problems and several-sample problems.The test statistics and refused domains for different tests are provided.At last,the stochastic simulation was used for feasibility.For restricting the probabilities of two types of error,this method can offer good results for samples with high quality.And the real error I is slightly above the nominal error I for general samples,this problems can be solved by increasing original sample size,decreasing the nominal error I and repeating tests.

关 键 词：多元有序数据 潜变量模型 轮廓分析 BOOTSTRAP方法 

分 类 号：O212[理学—概率论与数理统计] F224[理学—数学]