A theorem on the probabilities of large deviations for decomposable statistics that do not satisfy Cram\'er's condition
Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 87-94.

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We find the asymptotic behaviour of probabilities of large deviations of symmetric decomposable statistics in the context of the generalised allocation scheme where the Cramér condition is broken. We consider the case of the so-called small samples.
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A. V. Kolodzei. A theorem on the probabilities of large deviations for decomposable statistics that do not satisfy Cram\'er's condition. Diskretnaya Matematika, Tome 17 (2005) no. 2, pp. 87-94. http://geodesic.mathdoc.fr/item/DM_2005_17_2_a5/

[1] Kolchin V. F., “Odin klass predelnykh teorem dlya uslovnykh raspredelenii”, Lit. matem. sb., 8:1 (1968), 111–126

[2] Kolchin V. F., Sluchainye otobrazheniya, Nauka, Moskva, 1984 | MR

[3] Kolchin A. V., “Predelnye teoremy dlya obobschennoi skhemy razmescheniya”, Diskretnaya matematika, 15:4 (2003), 148–157 | MR | Zbl

[4] Medvedev Yu. I., “Nekotorye teoremy ob asimptoticheskom raspredelenii statistiki $\chi^2$”, Dokl. AN SSSR, 192:5 (1970), 997–989

[5] Ronzhin A. F., “Kriterii dlya obobschennykh skhem razmescheniya chastits”, Teoriya veroyatnostei i ee primeneniya, 33:1 (1988), 94–104 | MR

[6] Kramer G., “Ob odnoi novoi predelnoi teoreme teorii veroyatnostei”, Uspekhi matem. nauk, 1944, no. 10, 166–178

[7] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, Moskva, 1984

[8] Nagaev A. V., “Integralnye predelnye teoremy s uchetom veroyatnostei bolshikh uklonenii. I”, Teoriya veroyatnostei i ee primeneniya, 14:1 (1969), 51–63 | MR

[9] Fedoryuk M. V., Metod perevala, Nauka, Moskva, 1977 | MR

[10] Quine M. P., Robinson J., “Efficiencies of chi-square and likelihood ratio goodness-of-fit tests”, Ann. Stat., 13 (1985), 727–742 | DOI | MR | Zbl

[11] Ronzhin A. F., “Teorema o veroyatnostyakh bolshikh uklonenii dlya razdelimykh statistik i ee statisticheskoe prilozhenie”, Matem. zametki, 36:4 (1984), 603–615 | MR | Zbl