Abstract
In spatial statistics, it is usual to consider a Gaussian process for spatial latent variables. As the data often exhibit non-normality, we introduce a novel skew process, named hereafter Gaussian-log Gaussian convolution (GLGC) to construct latent spatial models which provide great flexibility in capturing skewness. Some properties including closed-form expressions for the moments and the skewness of the GLGC process are derived. Particularly, we show that the mean square continuity and differentiability of the GLGC process are established by those of the Gaussian and log-Gaussian processes considered in its structure. Moreover, the usefulness of the proposed approach is demonstrated through the analysis of spatial data, including mixed ordinal and continuous outcomes that are jointly modeled through a common latent process. A fully Bayesian analysis is adopted to make inference. Our methodology is illustrated with simulation experiments as well as an environmental data set.
Highlights
A popular approach for analyzing spatial data involves the introduction of latent variables
Motivated by analyzing a data set with mixed ordinal and continuous outcomes that are used to evaluate an unobservable process, we develop a Gaussian-log Gaussian convolution (GLGC) factor model to account for the inherent skewness in the data
In what is to follow, we develop a new class of skew spatial models relying on the log-normal distribution which is of major importance in probability and statistics
Summary
A popular approach for analyzing spatial data involves the introduction of latent variables. The use of the latent Gaussian models facilitates spatial analysis, the normality assumption might be overly restrictive in obtaining an accurate representation of the data structure. An alternative method of generating skewed distributions is to consider αW + Z, where Z has a symmetric distribution, but the non-negative variable W has a specified skewed distribution rather than being truncated An example of this is the normal-exponential convolution distribution (Aigner et al, 1977; Silver et al, 2009) in which Z is normal and W has an exponential distribution. We provide a brief discussion regarding how to extend the univariate skew model to the multivariate case
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