Pointwise estimator for the k-fold convolution of a distribution function
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.34, no.9-10, pp.1939-1956, 2005 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 9-10
- Publication Date: 2005
- Doi Number: 10.1080/03610920500201210
- Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.1939-1956
- Keywords: convolution, empirical df, renewal processes, V-statistics, RENEWAL FUNCTION, INVERSION
- Ankara University Affiliated: Yes
Abstract
This article is concerned with some parametric and nonparametric estimators for the k-fold convolution of a distribution function. An alternative estimator is proposed and its unbiasedness, asymptotic unbiasedness, and consistency properties are investigated. The asymptotic normality of this estimator is established. Some applications of the estimator are given in renewal processes. Finally, the computational procedures are described and the relative performance of these estimators for small sample sizes is investigated by a simulation study.