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On the efficiency of tests of fit based on the Deheuvels' empirical process
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 66-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider some goodness-of-fit tests which are functionals of the modified empirical process defined in the spirit of the paper [5]. We calculate their Bahadur efficiency for simple alternatives and find the conditions of local optimality for the analogue of Kolmogorov test. Bibl. – 10 titles. 
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Ya. Yu. Nikitin; P. P. Sporysheva. On the efficiency of tests of fit based on the Deheuvels' empirical process. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 13, Tome 361 (2008), pp. 66-77. http://geodesic.mathdoc.fr/item/ZNSL_2008_361_a4/

[1] A. Azzalini, “A class of distributions which includes the normal ones”, Scand. J. Stat., 12 (1985), 171–178 | MR | Zbl

[2] R. R. Bahadur, Some limit theorems in statistics, SIAM, Philadelphia, 1971 | MR | Zbl

[3] P. Billingsley, Convergence of probability measures, Wiley, 1968 | MR | Zbl

[4] A. N. Borodin, P. Salminen, Handbook of Brownian motion: Facts and formulae, 2nd ed., Birkhäuser, Basel, 2002 | MR | Zbl

[5] P. Deheuvels, “A Karhunen-Loève expansion for a mean-centered Brownian bridge”, Statistics and Probability Letters, 77 (2007), 1190–1200 | DOI | MR | Zbl

[6] A. Durio, Ya. Yu. Nikitin, “Local Bahadur efficiency of some goodness-of-fit tests under skew alternatives”, J. Statist. Plann. and Infer., 115:1 (2003), 171–179 | DOI | MR | Zbl

[7] M. Raghavachari, “On a theorem of Bahadur on the rate of convergence of test statistics”, Ann. Math. Stat., 41:4 (1970), 1695–1699 | DOI | MR | Zbl

[8] G. R. Shorack, J. A. Wellner, Empirical Processes with Applications to Statistics, Wiley, 1986 | MR | Zbl

[9] A. I. Nazarov, Ob odnom semeistve preobrazovanii gaussovskikh sluchainykh funktsii, SPbMS El. Prepr. Archive, No 2008-02, 2008; Теория вероятн. и ее примен., (сдано в печать)

[10] Y. Nikitin, Asymptotic efficiency of nonparametric tests, Cambridge University Press, 1995 | MR | Zbl