尤度比検定法に基づく正規母平均ベクトルに対する多変量片側検定方式の近似法について

摘要

In this study we consider a multivariate one-sided test for testing whether a normal mean vector having nonnegative components is equal to zero or not under the assumption that the covariance matrix is known. First, we discuss Kudo (1963)'s method based on the likelihood ratio test. Next, we discuss Tang et al. (1989)'s simple method which is called the approximate likelihood ratio test for the multivariate one-sided test. Furthermore, we discuss Glimm et al. (2002)'s method which modifies Tang et al. (1989)'s method. Specifically, we have two kinds of approximate methods for Kudo (1963)'s likelihood ratio test. We compare them in terms of numerical examples regarding critical values and power of the test.%成分がすべて負でない正規母平均ベクトルの零ベクトルとの差を調べるための多変量片側検定に対して分散共分散行列を既知と仮定した下で，Kudo（1963）が構築した尤度比検定法，Tang et al.（1989）が提案した尤度比検定法の近似法，さらにGlimm et al.（2002）が提案したTang et al.（1989）の近似法の修正について議論する.検出力についての数値例により手法を比較する.