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ASYMPTOTIC BEHAVIOR OF THE KOLMOGOROV-SMIRNOV TEST FOR POISSON PROCESSES WITH SCALE PARAMETER
Keywords:
inhomogeneous Poisson process, parametric basic hypothesis, Kolmogorov-Smirnov Mises test, asymptotically parameter free testDOI:
https://doi.org/10.17654/0972361724053Abstract
We studied the Kolmogorov-Smirnov test for inhomogeneous Poisson processes with parametric null hypothesis. The unknown parameter is a scale parameter. The construction of the test is based on the MLE of this parameter. The main result shows that due to the structure of the statistic, the substitution of the estimator in the place of the unknown parameter leads to the limit of the statistic test with distribution which does not depend on the unknown parameter.
Received: March 20, 2024
Revised: May 15, 2024
Accepted: June 13, 2024
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