Locally Optimal Tests for Multiparameter Hypotheses
提出了一种多参数情形下的局部最平均功效无偏检验方法，基于功效超曲面的平均曲率，相比现有方法具有更好的理论性质且易于构造临界区域，并给出了单变量和多元正态总体下的应用实例。
Abstract A generalization of a locally most powerful unbiased (LMPU) test, for the single parameter case, to the k-parameter case is proposed. In particular, we define a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared with the type C tests (Neyman and Pearson 1938) and the type D tests, LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions in practical situations. LMMPU tests are obtained for the important practical case (Perng and Littel 1976) of a two-parameter univariate normal population, for which Isaacson (1951, p. 233) was unable to find a type D test, and for the case of means of a multivariate normal population with independent coordinates.