Measuring the association of stationary point processes using spectral analysis techniques |
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Authors: | Dimitrios S Tsitsis George J Karavasilis Alexandros G Rigas |
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Institution: | 1. Department of Electrical and Computer Engineering, Democritus University of Thrace, Kimmeria, 67100, Xanthi, Greece
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Abstract: | In this work we focus on relationships between stationary point process using spectral analysis techniques. The evaluation
of these relationships is accomplished with the help of the product ratio of association (PRA), which is based on the cumulant
densities of the point processes. The estimation procedure is obtained by smoothing the periodogram statistic, a function
of the frequency domain. It is proved that the asymptotic distribution of the square root of the estimated PRA is Normal with
a constant variance. Statistical tests for hypotheses concerning the independence of two point processes and the characterization
of a Poisson process are proposed. Furthermore, approximate 95% pointwise confidence interval can be obtained for the estimated
PRA. These results can be applied on stochastic systems involving as input and output stationary point processes. An illustrative
example from the framework of neurophysiology is presented. |
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