Scholarlink

<p>This paper studies hypothesis testing for structured scale matrices in the multivariate <i>t</i> distribution. We develop likelihood ratio and Rao score tests for general structural constraints on the scale matrix and derive the Wald test for hypotheses in which the scale matrix is restricted to a quadratic subspace. The latter class includes, in particular, diagonality, sphericity, compound symmetry, circular Toeplitz structures, and their block extensions with structured subblocks. Since the construction of the test statistics requires maximum likelihood estimation, we derive the likelihood equations under quadratic subspace restrictions. Although likelihood ratio and score tests have been investigated for covariance structure in the multivariate normal model, the Wald test has not been developed in that setting. Because the multivariate normal distribution arises as a limiting case of the multivariate <i>t</i> model, our results also provide a new contribution to the normal framework. Finite sample performance is examined via simulation, and a real data example illustrates the proposed methodology.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Estimation and testing of the commutative quadratic covariance structure under multivariate t distribution

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月18日

查看全文
  • Katarzyna Filipiak,
  • Daniel Klein,
  • Stepan Mazur,
  • Monika Mokrzycka

摘要

This paper studies hypothesis testing for structured scale matrices in the multivariate t distribution. We develop likelihood ratio and Rao score tests for general structural constraints on the scale matrix and derive the Wald test for hypotheses in which the scale matrix is restricted to a quadratic subspace. The latter class includes, in particular, diagonality, sphericity, compound symmetry, circular Toeplitz structures, and their block extensions with structured subblocks. Since the construction of the test statistics requires maximum likelihood estimation, we derive the likelihood equations under quadratic subspace restrictions. Although likelihood ratio and score tests have been investigated for covariance structure in the multivariate normal model, the Wald test has not been developed in that setting. Because the multivariate normal distribution arises as a limiting case of the multivariate t model, our results also provide a new contribution to the normal framework. Finite sample performance is examined via simulation, and a real data example illustrates the proposed methodology.