Recently some authors have introduced in the literature stationary stochastic processes, in the time and in the spatial domains, whose finite-dimensional marginal distributions are multivariate skew-normal. Here we show with a counter-example that the characterizations of these processes are not valid and so that these processes do not exist. In particular, we show through a marginalization argument that the set of finite-dimensional marginal distributions of these processes is not self-coherent. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.

On the existence of some skew-normal stationary processes

MINOZZO, Marco;
2012

Abstract

Recently some authors have introduced in the literature stationary stochastic processes, in the time and in the spatial domains, whose finite-dimensional marginal distributions are multivariate skew-normal. Here we show with a counter-example that the characterizations of these processes are not valid and so that these processes do not exist. In particular, we show through a marginalization argument that the set of finite-dimensional marginal distributions of these processes is not self-coherent. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.
Autocorrelation function; Generalized linear mixed model; Geostatistics; Multivariate skew-normal distribution; Spatial process; Stationary process
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/474179
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