Abstract

RODRIGUEZ-BERRIO, Felipe; RODRIGUEZ-CORTES, Francisco J.; MATEU, Jorge  and  ADELFIO, Giada. On Some Statistical Properties of the Spatio-Temporal Product Density. Rev.Colomb.Estad. [online]. 2021, vol.44, n.1, pp.23-41.  Epub Feb 25, 2021. ISSN 0120-1751.  https://doi.org/10.15446/rce.v44n1.84779.

We present an extension of the non-parametric edge-corrected Ohser-type kernel estimator for the spatio-temporal product density function. We derive the mean and variance of the estimator and give a closed-form approximation for a spatio-temporal Poisson point process. Asymptotic properties of this second-order characteristic are derived, using an approach based on martingale theory. Taking advantage of the convergence to normality, confidence surfaces under the homogeneous Poisson process are built. A simulation study is presented to compare our approximation for the variance with Monte Carlo estimated values. Finally, we apply the resulting estimator and its properties to analyse the spatio-temporal distribution of the invasive meningococcal disease in the Rhineland Regional Council in Germany.

Keywords : Envelope; Invasive meningococcal disease; Lindeberg condition; Ohser-type estimator; Second-order product density.

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