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Title: An EM-type algorithm for maximum likelihood estimation of spatial models with positional errors Authors:  Marco Bee - University of Trento (Italy) [presenting]
Giuseppe Espa - University of Trento (Italy)
Diego Giuliani - University of Trento (Italy)
Maria Michela Dickson - University of Trento (Italy)
Emanuele Taufer - University of Trento (Italy)
Flavio Santi - University of Trento (Italy)
Abstract: Positional errors are often encountered in spatial statistics. The coordinates $c_i^*$ of not properly located observations can be written as $c_i^*=c_i+m_i$, where $c_i$ are the true (but unobserved) coordinates and $m_i$ is a bivariate normal random vector which models the error. Given that the $m_i$s can be interpreted as missing data, an estimation method based on the EM algorithm is developed. The impact of various hypotheses on the parameters of $m$ (zero or non-zero mean, heteroskedasticity and/or dependence of the two components) is studied via simulation. The details of the algorithm are worked out in the framework of the Spatial Lag model, with a connectivity matrix defined as a non-linear function of the Euclidean distance between the observations, but can easily be extended to other spatial statistics models. From the technical point of view, both the E and the M step are not in closed form. A possible solution consists of computing the E-step by Monte Carlo simulation and using standard numerical optimization routines for the M-step.