The testing problem on the first-order autoregressive parameter in finite sample case is considered. The innovations are distributed according to the exponential distribution. The aim of this paper is to study how much the size of this test changes when, at some time k, an innovation outlier contaminant occurs. We show that the test is rather sensitive to these changes.
The locally most powerful (LMP) tests of the hypothesis against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood...
The two-sample Lepage test, devised for testing equality of the location and scale parameters against the alternative that at least for one of the parameters the equality does not hold, is extended to the general case of sampled populations. It is shown that its limiting distribution is the chi-square distribution with degrees of freedom. This -sample statistic is shown to yield consistent test and a formula for its noncentrality parameter under Pitman alternatives is derived. For some particular...