Modeling and estimation of some non Gaussian random fields
In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields wi...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2018 |
| País: | Chile |
| OAI Identifier: | oai:repositorio.anid.cl:10533/214737 |
| Acceso en línea: | https://hdl.handle.net/10533/214737 |
| Access Level: | acceso abierto |
| Palabra clave: | Ingeniería y Tecnología Otras Ingenierías y Tecnologías |
| Sumario: | In this work, we propose two types of models for the analysis of regression and dependence of positive and continuous spatio-temporal data, and of continuous spatio-temporal data with possible asymmetry and/or heavy tails. For the first case, we propose two (possibly non stationary) random fields with Gamma and Weibull marginals. Both random fields are obtained transforming a rescaled sum of independent copies of squared Gaussian random fields. For the second case, we propose a random field with t marginal distribution. We then consider two possible generalizations allowing for possible asymmetry. In the first approach we obtain a skew-t random field mixing a skew Gaussian random field with an inverse square root Gamma random field. In the second approach we obtain a two piece t random field mixing a specific binary discrete random field with half-t random field. We study the associated second order properties and in the stationary case, the geometrical properties. Since maximum likelihood estimation is computationally unfeasible, even for relatively small data-set, we propose the use of the pairwise likelihood. The effectiveness of our proposal for the gamma and weibull cases, is illustrated through a simulation study and a re-analysis of the Irish Wind speed data (Haslett and Raftery, 1989) without considering any prior transformation of the data as in previous statistical analysis. For the t and asymmetric t cases we present a simulated study in order to show the performance of our method. |
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