Gaussian Scale Mixtures

Felgueiras, Miguel Martins; Martins, João Paulo; Santos, Rui Filipe

http://hdl.handle.net/10400.8/14321

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Authors

Felgueiras, Miguel Martins

Martins, João Paulo

Santos, Rui Filipe

Abstract(s)

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.