1925

Автор(ы): 

Автор(ов): 

2

Параметры публикации

Тип публикации: 

Статья в журнале/сборнике

Название: 

Nonparametric Estimation of the Renewal Function by Empirical Data

Наименование источника: 

  • Stochastic Models

Обозначение и номер тома: 

22:2

Город: 

  • Melbourne

Издательство: 

  • Taylor and Francis

Год издания: 

2006

Страницы: 

175-199
Аннотация
We consider an estimate of the renewal function (rf) $H(t)$ using alimited number of independent observations of the interarrival timesfor an unknown interarrival-time distribution (itd). Thenonparametric estimate is derived from the rf-representation as series of distribution functions (dfs) ofconsecutive arrival times using a finite summation and approximations of the latter by empirical dfs.Due to the limited number of observed interarrival times theestimate is accurate just for closed time intervals $[0,t]$.An important aspect is given by the selection of an optimalnumber of terms $k$ of the finite sum. Here two methods are proposed: (1) an a priori choice of $k$ as function of the sample size $l$ which provides almost surely (a.s.) the uniform convergence of the estimate to the rf for light- and heavy-tailed itdsif the time interval is not too large, and (2) a data-dependentselection of $k$ by a bootstrap method.To evaluate boththe efficiency of the estimate and the selection methods of$k$, a Monte Carlo study is performed.

Библиографическая ссылка: 

Маркович Н.М., Krieger U. R. Nonparametric Estimation of the Renewal Function by Empirical Data // Stochastic Models. 2006. 22:2. С. 175-199.