Influence diagnostics in Gaussian spatial-temporal linear models with separable covariance

Abstract

In recent decades, there has been a growing interest in modeling spatial-temporal data, which can be found in many fields including geoscience, meteorology and ecology, among many others. The spatial-temporal dependence structure modeling, using a random field approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. Our proposal is to extend the results of Uribe-Opazo et al. (J Appl Stat 39:615-630, 2012) and De Bastiani et al. (Test 24:322-340, 2015) in the studies of diagnostic techniques to assess the sensitivity of the maximum likelihood estimators to small perturbations in the response variable for the spatial-temporal linear models with separable covariance. The method's viability is illustrated in a simulation study, and in an application to eggs anchovy (Engraulis ringens) abundance data in ichthyoplankton surveys from the northern zone of Chile. The results show that the proposed methodology allows to detect influential observations in a spatial-temporal data set when their covariances are separable.