Abstract
Consider processes formed as products of independent Poisson and symmetrized Poisson processes. This paper provides exponential bounds for the tail probabilities of statistics representable as integrals of bounded functions with respect to such product processes. In the derivations, tail probability bounds are also obtained for product empirical measures. Such processes arise in tests of independence. A generalization of the Hanson-Wright inequality for quadratic forms is used in the symmetric case. The paper also provides some reasonably tractable approximations to the more general bounds that are derived first.
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Kwon, J.S., Pyke, R. (1996). Probability Bounds for Product Poisson Processes. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_10
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DOI: https://doi.org/10.1007/978-1-4612-0749-8_10
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