On extreme value asymptotics for increments of renewal processes

Via strong invariance, a number of weak asymptotics are established for certain maximum increments of renewal counting processes. The results are suggested to serve as asymptotic testing devices for detecting changes in the intensity of the underlying renewal process. Some simulations are presented...

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Bibliographic Details
Published in:Journal of statistical planning and inference 1995, Vol.45 (1), p.301-312
Main Authors: Steinebach, Josef, Eastwood, Vera R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Extreme value asymptotics
Gumbel type limiting distributions
Increments of renewal processes
Invariance principles
Limit theorems
Mathematics
Pontograms
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Strong approximations
Weighted embeddings
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Summary:Via strong invariance, a number of weak asymptotics are established for certain maximum increments of renewal counting processes. The results are suggested to serve as asymptotic testing devices for detecting changes in the intensity of the underlying renewal process. Some simulations are presented to study the finite sample properties of the proposed test statistics, and to provide asymptotic critical values.
ISSN:0378-3758
1873-1171
DOI:10.1016/0378-3758(94)00079-4