Geodesic
On a~quadratic measure of the deviation of projection density estimates
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 864-871

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Limiting law problems for the distributions of squared norms of estimation errors (1) are considered. The behaviour of the goodness-of-fit test based on these statistics being studied, the limiting power for some local alternatives is calculated. The goodness-of-fit test based on density estimates is shown to be equivalent to the $\chi^2$-test. 
@article{TVP_1976_21_4_a17,
     author = {E. A. Nadaraya},
     title = {On a~quadratic measure of the deviation of projection density estimates},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {864--871},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a17/}
}
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E. A. Nadaraya. On a~quadratic measure of the deviation of projection density estimates. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 4, pp. 864-871. http://geodesic.mathdoc.fr/item/TVP_1976_21_4_a17/