Gaussian Scale Mixtures Miguel Martins Felgueiras 1 *, João Paulo Martins**, Rui Filipe Santos**
* CEAUL Lisbon and ESTG, CIGS, Polytechnic Institute of Leiria, Portugal ** CEAUL Lisbon and ESTG, Polytechnic Institute of Leiria, Portugal
Abstract: In this paper we present a parsimonious approximation of a Gaussian mixture when its components share a common mean value, i.e. a scale mixture. We show that a shifted and scaled Student’s t-distribution can be approximated to this type of mixture, and use the result to develop a hypothesis test for the equality of the components mean value. A simulation study to check the quality of the approximation is also provided, together with an application to logarithmic daily returns.