A Nonparametric Coefficient

Ronny Vallejos (), Felipe Osorio () and Moreno Bevilacqua
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Ronny Vallejos: Federico Santa María Technical University, Department of Mathematics
Felipe Osorio: Federico Santa María Technical University, Department of Mathematics
Moreno Bevilacqua: Universidad Adolfo Ibañez, Faculty of Engineering and Sciences

Chapter Chapter 6 in Spatial Relationships Between Two Georeferenced Variables, 2020, pp 115-130 from Springer

Abstract: Abstract The goal of the current chapter is to introduce a nonparametric version of the codispersion coefficient. Extensions of this nature have previously been considered in the spatial statistics literature. For example, Hall et al. (1994) studied nonparametric estimations of the covariance function. Nonparametric estimations of the semivariogram were examined by Garcia-Soidan et al. (2004), Yu et al. (2007), and Garcia-Soidan (2007), among others. After giving preliminaries notions of kernels, we introduce a nonparametric coefficient based on the ideas first introduced by Nadaraya (1965) and Watson (1964). Asymptotic expressions for the expected value, variance and mean square error of the proposed estimator will be provided. The proofs will be relegated to the Appendix A. In Sect. 6.5 a bandwidth selection method associated with the later estimation is depicted. We report the results of the Monte Carlo simulation studies in Sect. 6.6. The chapter ends with applications to real data to illustrate how the nonparametric estimator works in practice.

Date: 2020
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DOI: 10.1007/978-3-030-56681-4_6

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