Geodesic
Large deviations and asymptotic efficiency of integral type statistics.~I
Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 175-187

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We obtain rough asymptotics for probabilities of large deviations of $\omega^2$-type integral statistics and their analogues for Poisson sample size. An approach due to Sanov is used so that this asymptotics depend on a solution of some extremal problem. The latter is solved with the aid of bifurcation theory. 
@article{ZNSL_1979_85_a13,
     author = {Ya. Yu. Nikitin},
     title = {Large deviations and asymptotic efficiency of integral type {statistics.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {175--187},
     publisher = {mathdoc},
     volume = {85},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a13/}
}
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Ya. Yu. Nikitin. Large deviations and asymptotic efficiency of integral type statistics.~I. Zapiski Nauchnykh Seminarov POMI, Investigations in the theory of probability distributions. Part IV, Tome 85 (1979), pp. 175-187. http://geodesic.mathdoc.fr/item/ZNSL_1979_85_a13/