The Locally Most Powerful Unbiased Test for the location parameter of von Mises Distribution

在最近幾年, 方向資料 (direction data) 的研究已經引起愈來愈多統計 學者注意. 在本篇論文中, 我們將探討二度空間上的方向資料問題, 並稱 之為圓形資料 (circular data).對於翁敏士分布 (von Mises distribution) 位置參數是否為零的假設檢定問題, 馬迪亞 (Madia) 在 1972年的著作上證明不存在全區域最有效率測試統計量 (uniformally most powerful test), 同時也提出可能性比率測試統計量 (likelihood ratio test) 以解決這個問題. 我們將在以下文章提出區域 最有效率不偏測試統計量 (locally most powerful unbiased test), 並 對這二個測試統計量做一比較.The research of directional data has attracted more and more attention of statisticans in the recent years. We will handle the problem about the two-dimensional data throughout this context and refer such data as the circular data. Having a lot of important characterization as the normal distribution does in the linear statistics, the von Mises distribution has a great importance in the circular data. It makes people to devote a lot of eff- orts in the dealing with the investigation of this distribution. For the problem of testing whether a given sample of von Mises dirtribution has zero direction, when the concentration parameter is fixed, Madia (p.136,(1972)) proved there is no UMP test. And Madia (p.137,(1972)) also proposed the likelihood ratio test. In this paper, we are about to employ the concept of locally most powerful unbiased test to derive a test and excute some comparsions between these two tests