Model testing for spatial strong mixing data

R. Ignaccolo 1 and N. Ribeccoy 2
1 Dipartimento di Statistica e Matematica Applicata
Università degli Studi di Torino, Italy
e-mail: ignaccolo@econ.unito.it
2 Dipartimento di Scienze Statistiche
Università degli Studi di Bari, Italy
e-mail: ribecco@dss.uniba.it

Abstract
In analysing the distribution of a variable in a space, each value is subject not only to the source of the phenomenon but also to its localisation. In this paper, we t the model of the distribution, taking explicitly into account the spatial autocorrelation among the observed data. To this end we rst suppose that the observations are generated by a strong-mixing random eld. Then, after estimating the density of the considered variable, we construct a test statistics in order to verify the goodness of t of the observed spatial data. The proposed class of tests is a generalization of the classical chi-square-test and of the Neyman smooth test. The asymptotic behaviour of the test is analysed and some indications about its implementation are provided.

Keywords: goodness of t; correlated data; spatial process; mixing random eld.

In: McRoberts, R. et al. (eds).  Proceedings of the joint meeting of The 6th International Symposium On Spatial Accuracy Assessment In Natural Resources and Environmental Sciences and The 15th Annual Conference of The International Environmetrics Society, June 28 – July 1 2004, Portland, Maine, USA.

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