Moment-based oscillation properties of mixture models

• 成果类型: Article
• 署名作者: Lindsay, B; Roeder, K
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 378-386
• 关键词: exponential-families

摘要

Consider finite mixture models of the form g(x; Q) = integral f(x; theta)dQ(theta), where f is a parametric density and Q is a discrete probability measure. An important and difficult statistical problem concerns the determination of the number of support points (usually known as components) of Q from a sample of observations from g. For an important class of exponential family models we have the following result: if P has more than p components and Q is an appropriately chosen p-component approximation of P, then g(x; P) - g(x; Q) demonstrates a prescribed sign change behavior, as does the corresponding difference in the distribution functions. These strong structural properties have implications for diagnostic plots for the number of components in a finite mixture.