On Some Statistical Properties of the Spatio-Temporal Product Density
- Autori: Rodrìguez-Berrio F; RodrÃguez-Cortés F J; Mateu J; Adelfio G
- Anno di pubblicazione: 2021
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/512781
Abstract
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.