Gaussian Scale Mixtures

Gaussian Scale Mixtures Miguel Martins Felgueiras 1 *, Jo´┐Żo 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.

Keywords: Gaussian scale mixture, Student’s t-distribution, log-returns, simulation.
Mathematics Subject Classification: 60E05; 62P20.


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