J. Japan Statist. Soc., Vol. 33 (No. 2), pp. 169-180, 2003

Some Properties of the Point Optimal Invariant Test for the Constancy of Parameters

Eiji Kurozumi

Abstract. In this paper we consider the time-varying parameter model. Since there is no uniformly most powerful test for the constancy of parameters, the locally best invariant (LBI) test has often been considered in the literature, including the study by Nabeya and Tanaka (1988). We show the existence of the limiting distribution of the point optimal invariant (POI) test statistic when we can derive the limiting distribution of the LBI test statistic. We prove that the limiting characteristic function of the POI test statistic can be expressed using that of the LBI test statistic.

Key words and phrases: Characteristic function, constancy of parameters, locally best invariant test, point optimal invariant test, power envelope.

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