Asymptotic Normality of Binned Kernel Density Estimators for Non-stationary Dependent Random Variables

Michel Harel (), Jean-François Lenain () and Joseph Ngatchou-Wandji ()
Additional contact information
Michel Harel: ÉSPÉ de Limoges
Jean-François Lenain: Faculté des Sciences et Techniques
Joseph Ngatchou-Wandji: Université de Lorraine, EHESP de Rennes, Institut Élie Cartan de Lorraine

A chapter in Mathematical Statistics and Limit Theorems, 2015, pp 167-187 from Springer

Abstract: Abstract We establish the asymptotic normality of binned kernel density estimators for a sequence of dependent and nonstationary random variables converging to a sequence of stationary random variables. We compute the asymptotic variance of a suitably normalized binned kernel density estimator and study its absolute third-order moment. Then, we show that its characteristic function tends to that of a zero-mean Gaussian random variable (rv). We illustrate our results with a simulation experiment.

Keywords: Mean Square Error; Central Limit Theorem; Asymptotic Normality; Confidence Band; Stationary Time Series (search for similar items in EconPapers)
Date: 2015
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12442-1_10

Ordering information: This item can be ordered from
http://www.springer.com/9783319124421

DOI: 10.1007/978-3-319-12442-1_10

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().