Geodesic
On determination of the order of a parabolic regression equation
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 718-727 
G. N. Boganik. On determination of the order of a parabolic regression equation. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 4, pp. 718-727. http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a9/
@article{TVP_1967_12_4_a9,
     author = {G. N. Boganik},
     title = {On determination of the order of a~parabolic regression equation},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {718--727},
     year = {1967},
     volume = {12},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_4_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of testing of statistical hypotheses about the proper degree of a parabolic regression equation is considered. There has not been any appropriate test statistic for an important case when a sequence of single observations with an unknown variance of their random errors is given. Here such a statistic is suggested and the first two moments of its distribution are obtained. The new test is shown to be asymptotically more powerful than the $\chi^2$-test.