Asymptotic behaviour of binned kernel density estimators for locally non-stationary random fields

• Published in: Journal of nonparametric statistics Vol. 28; no. 2; pp. 296 - 321
• Main Authors: Harel, Michel, Lenain, Jean-François, Ngatchou-Wandji, Joseph
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02-04-2016; Taylor & Francis Ltd; American Statistical Association
• Subjects: Applications; Asymptotic properties; bias; binned kernel density estimation; centrallimit theorem; Density; Epidemiology; Estimators; Fields (mathematics); Kernels; locally non-stationary random fields; Mathematics; Methodology; Nonparametric statistics; Simulation; Statistics; Statistics Theory; Theorems; Tuberculosis
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2016.1163351

We investigate the asymptotic behaviour of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. We focus on the study of the bias and the asymptotic normality of the estimators. A simulation experiment conducted shows that both the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. We apply our results to the 2002 incidence rates of tuberculosis in the departments of France.