Best Conditional Tests for Separate Families of Hypotheses
研究了如何将随机变量的概率密度函数分配给两个分离的分布族之一，构建最佳相似检验，并给出了广义指数型分布族下检验统计量的易得条件，通过实例和模拟比较了精确最佳检验与渐近检验在小样本下的表现。
SUMMARY We consider, from the viewpoint of hypotheses testing, the problem of assigning the probability density function of a random variable X to one of two separate families of distributions. Our aim is to study the possibility of constructing best similar tests. For this, we characterize sufficient statistics for the union of the two families; completeness is also studied. We state conditions under which the test statistics are easily obtainable when both families are of the generalized exponential type. As an illustration, many examples are given solving both new and previously worked problems of choice between separate families of hypotheses. The relative merits of the exact best test and of asymptotic tests are empirically investigated in small samples when testing for the log-normal versus the gamma distribution.