Edgeworth expansions for compound poisson processes and the bootstrap

• Published in: Annals of the Institute of Statistical Mathematics Vol. 55; no. 1; pp. 83 - 94
• Main Authors: BABU, Gutti Jogesh, SINGH, Kesar, YANING YANG
• Format: Journal Article
• Language: English
• Published: Tokyo Kluwer 01-03-2003; Dordrecht Springer Nature B.V
• Subjects: Distribution theory; Exact sciences and technology; Mathematical analysis; Mathematics; Nonparametric inference; Parametric inference; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications); Statistics; Compound process; Statistical distribution; Edgeworth expansion; Renewal process; Non parametric estimation; Statistical estimation; Mean estimation; Poisson process; Confidence interval; Coefficient of skewness; Skewness; Bootstrap; Jackknife method; Approximate solution; Mathematical expansion; Resampling method; Corrections; Cumulant
• ISSN: 0020-3157; 1572-9052
• DOI: 10.1007/BF02530486

One-term Edgeworth Expansions for the studentized version of compound Poisson processes are developed. For a suitably defined bootstrap in this context, the so called one-term Edgeworth correction by bootstrap is also established. The results are applicable for constructing second-order correct confidence intervals (which make correction for skewness) for the parameter "mean reward per unit time". [PUBLICATION ABSTRACT]