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

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 bo...

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Bibliographic Details
Published in:Journal of nonparametric statistics 2016-04, Vol.28 (2), p.296-321
Main Authors: Harel, Michel, Lenain, Jean-François, Ngatchou-Wandji, Joseph
Format: Article
Language:English
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
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Summary: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.
ISSN:1048-5252
1029-0311
DOI:10.1080/10485252.2016.1163351