Best Conditional Tests for Separate Families of Hypotheses
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1990 · Volume 52 · Issue 1
DOI: 10.1111/j.2517-6161.1990.tb01776.x
Abstract
We consider, from the viewpoint of hypotheses testing, the problem of assigning the probability density function of a random variableXto 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.
Keywords
completeness, conditional tests, generalized exponential families, separate families, similar tests, sufficiency
Enable JavaScript for citation tools and additional paper interactions.