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

Abstract

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.

Keywords:

• binned kernel density estimation
• locally non-stationary random fields
• bias
• centrallimit theorem

AMS Subject Classification:

• 60G10
• 62M30
• 62N02
• 62G07

Acknowledgments

We thank the Editor, the Associate Editor, and the referees for their constructive remarks and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.