# 1925

## 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

22:2

• Melbourne

## Издательство:

• Taylor and Francis

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.