Geodesic
Exact $L_2$-small ball asymptotics for some Durbin processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 211-233 Cet article a éte moissonné depuis la source Math-Net.Ru

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We find the exact $L_2$-small ball asymptotics for some Durbin processes. These processes are finite dimentional perturbations of the Brownian bridge $B(t)$ and naturally appear in statistics as limit ones when building goodness-of-fit tests of $\omega^2$-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 was developed. Due to this, it is possible to calculate the asymptotics of small deviations for Durbin processes for certain distributions (Laplace, logistic, Gumbel, gamma). 
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     title = {Exact $L_2$-small ball asymptotics for some {Durbin} processes},
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Yu. P. Petrova. Exact $L_2$-small ball asymptotics for some Durbin processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 26, Tome 466 (2017), pp. 211-233. http://geodesic.mathdoc.fr/item/ZNSL_2017_466_a14/

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