Geodesic
Kolmogorov tests of normality based on some variants of Polya's characterization
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 263-273

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Two variants of Kolmogorov-type $U$-empirical tests of normality are studied. They are based on the variants of famous Polya's characterization of the normal law. We calculate their local Bahadur efficiency against location, skew and Lehmann alternatives and find that the integral tests are usually more efficient. 
@article{ZNSL_2015_441_a15,
     author = {V. V. Litvinova and Ya. Yu. Nikitin},
     title = {Kolmogorov tests of normality based on some variants of {Polya's} characterization},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {263--273},
     publisher = {mathdoc},
     volume = {441},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a15/}
}
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V. V. Litvinova; Ya. Yu. Nikitin. Kolmogorov tests of normality based on some variants of Polya's characterization. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 22, Tome 441 (2015), pp. 263-273. http://geodesic.mathdoc.fr/item/ZNSL_2015_441_a15/