Asymptotic behavior of nonparametric estimators of the two-dimensional and bivariate renewal functions

We study the asymptotic behavior of the two-dimensional or bivariate nonparametric estimators of the renewal function associated to a sequence of absolutely continuous non-negative random vectors. We prove that these estimators are consistent and unbiased when the random vectors are independent and...

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Veröffentlicht in:	Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems 2019-10, Vol.22 (3), p.499-523
Hauptverfasser:	Harel, Michel, Andriamampionona, Livasoa, Harison, Victor
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic properties Bivariate analysis Estimating techniques Estimators Mathematics Mathematics and Statistics Nonparametric statistics Normality Probability Theory and Stochastic Processes Regression analysis Statistical Theory and Methods
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Beschreibung
Zusammenfassung:	We study the asymptotic behavior of the two-dimensional or bivariate nonparametric estimators of the renewal function associated to a sequence of absolutely continuous non-negative random vectors. We prove that these estimators are consistent and unbiased when the random vectors are independent and identically distributed but are neither consistent nor unbiased when the random vectors are strictly stationary absolutely regular. The asymptotic normality of these estimators on the space R + 2 is established when the random vectors are independent and identically distributed.
ISSN:	1387-0874 1572-9311
DOI:	10.1007/s11203-018-9192-x