An improved sib-pair test for linkage is introduced which is superior to the previously proposed tests. The test is derived from the standard chi-squared goodness of fit statistic by restricting the alternative hypothesis to the genetically possible. Critical values are given and exact power comparisons are made with the previously proposed tests. The new test is shown to be more powerful for f...

The uniformly most powerful invariant (UMPI) test is derived for detecting a target with unknown location in a noise sequence. This test has the property that for each possible target location it has the greatest power of all tests which are invariant to cyclic permutations of the observations. The test is compared to the generalised likelihood ratio test (GLRT), which is commonly used as a sol...

We consider univariate goodness-of-fit tests. A result stating the non-existence of a uniformly most powerful test, for all combinations of null and alternative distributions, which are completely specified, is given.