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Second-Order Efficient Test for Inhomogeneous Poisson Processes

Authors:	Fazli Kh

Institution:	(1) Laboratoire de Statistique et Processus, Université du Maine, 72085 Le Mans, Cedex 9, France

Abstract:	We observe a realization X ⁽ⁿ⁾ of a Poisson process on the set ${\mathbb{A}_{n} \subset \mathbb{R}^d }$ with intensity function ${S\left(\vartheta,x\right), x\in \mathbb{A}_{n}}$ depending on the unknown real parameter ${\vartheta \in \Theta \subseteq \mathbb{R}^{1}}$ . Based on X ⁽ⁿ⁾ we test simple null hypothesis ${{\cal H}_{0}: \vartheta = \vartheta_{0}}$ against one sided alternative ${{\cal H}_{1}: \vartheta < \vartheta_{0}}$ for given $\vartheta_{0}$ . 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.

Keywords:	inhomogeneous Poisson processes hypotheses testing first and second order efficiency locally asymptotically uniformly most powerful test
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