Geodesic
Chi-squared test for testing of homogeneity
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 160-180

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We provide necessary and sufficient conditions of uniform consistency of nonparametric sets of alternatives of chi-squared test for testing of hypothesis of homogeneity. The number of cells of chi-squared test increases with sample size growth. Nonparametric sets of alternatives can be defined both in terms of densities and distribution functions. 
@article{ZNSL_2021_501_a10,
     author = {M. S. Ermakov},
     title = {Chi-squared test for testing of homogeneity},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {160--180},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a10/}
}
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M. S. Ermakov. Chi-squared test for testing of homogeneity. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 160-180. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a10/