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We find the exact L2-small ball asymptotics for some Durbin processes. These processes are finitedimensional perturbations of a Brownian bridge B(t) and naturally appear in statistics as limit ones when one constructs goodness-of-fit tests of ω2-type for testing a sample for some distribution with estimated parameters. Earlier, in the work of Nazarov and Petrova, Kac–Kiefer–Wolfowitz processes (which correspond for testing normality) were considered, where a technique for obtaining asymptotics of oscillating integrals with a slowly varying amplitude has been developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma).
Original language | English |
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Pages (from-to) | 842-857 |
Number of pages | 16 |
Journal | Journal of Mathematical Sciences |
Volume | 244 |
Issue number | 5 |
DOIs | |
State | Published - 1 Feb 2020 |
ID: 78547875