Testing for Unobserved Heterogeneity via k-means Clustering
提出一种分割样本检验方法，用于判断数据是否应拒绝单一聚类的原假设（即数据同质），适用于多种聚类场景，如小时间序列维度或非均值参数聚类。
Clustering methods such as k-means have found widespread use in a variety of applications. This article proposes a split-sample testing procedure to determine whether a null hypothesis of a single cluster, indicating homogeneity of the data, can be rejected in favor of multiple clusters. The test is simple to implement, valid under mild conditions (including nonnormality, and heterogeneity of the data in aspects beyond those in the clustering analysis), and applicable in a range of contexts (including clustering when the time series dimension is small, or clustering on parameters other than the mean). We verify that the test has good size control in finite samples, and we illustrate the test in applications to clustering vehicle manufacturers and U.S. mutual funds.