خسرو فضلی

We observe a realization X(n) of a Poisson process on the set An ⊂ Rd with intensity function S (ϑ, x) , x ∈An depending on the unknown real parameter ϑ ∈⊆R1. Based on X(n) we test simple null hypothesis H0: ϑ = ϑ0 against one sided alternative H1:ϑ >ϑ0 for given ϑ0. We improve the level of the well-known locally asymptotically uniformly most powerful (LAUMP) test by using the Edgeworth type expansion for stochastic integral. We show that the improved test is second-order efficient under certain regularity conditions.