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

Michel Harel (), Livasoa Andriamampionona () and Victor Harison ()
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Michel Harel: UMR5219 UPS
Livasoa Andriamampionona: University of Antananarivo
Victor Harison: University of Antananarivo

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 6, 499-523

Abstract: Abstract 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 $$\mathbb {R}_{+}^{2}$$ R + 2 is established when the random vectors are independent and identically distributed.

Keywords: U-statistics; Almost sure convergence; Asymptotic normality; Renewal function; Renewal process; Absolute regularity; Primary 60F05; 60F15; Secondary 62G05; 62G20; 62G30; 62H12 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11203-018-9192-x

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