Asymptotic Behavior of a Nonparametric Estimator of the Renewal Function for Random Fields

Abstract

In this paper, we study the asymptotic normality of a nonparametric estimator of the renewal function associated with a sequence of absolutely continuous nonnegative two-dimensional random fields. We prove that this estimator is asymptotically unbiased. The asymptotic normality of this estimator is established.

Keywords

• random fields
• renewal function
• renewal process
• asymptotic normality