Identify the source of spikes: factor or mixture?
研究高维线性潜变量模型中潜变量是连续还是分类的问题，通过分析奇异向量的渐近行为提出基于特征向量分位数差异的检验统计量，并验证其有效性。
Summary We consider the problem of identifying the pattern of latent variables in high-dimensional linear latent variable models, which can also be interpreted as determining the source of spiked singular values in the data matrix. Specifically, we test whether the latent variables are continuous or categorical, a distinction which is crucial for data interpretation but challenging in the high-dimensional regime. To address this inference problem, we analyze the asymptotic behavior of empirical measures associated with singular vectors corresponding to large spiked singular values. Leveraging these insights,we propose novel test statistics based on the eigenvector quantile differences and establish their theoretical performance under the null hypothesis. Simulation studies and real data analyses demonstrate the effectiveness and practical utility of our method.