Geodesic
Test of symmetry in nonparametric regression
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 110-130

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The minimax properties of a test verifying a symmetry of an unknown regression function $f$ from $n$ independent observations are studied. The underlying design is assumed to be random and independent of the noise in observations. The function $f$ belongs to a ball in a Hölder space of regularity $\beta$. The null hypothesis accepts that $f$ is symmetric. We test this hypothesis versus the alternative that the $L_2$ distance from $f$ to the set of symmetric functions exceeds $\sqrt{r_n/2}$. As shown, these hypotheses can be tested consistently when $r_n=O(n^{-4\beta/(4\beta+1)})$.
Keywords: minimax hypothesis testing, minimax decision, Hölder class. 
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     author = {F. Leblanc and O. V. Lepskiǐ},
     title = {Test of symmetry in nonparametric regression},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {110--130},
     publisher = {mathdoc},
     volume = {47},
     number = {1},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a7/}
}
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F. Leblanc; O. V. Lepskiǐ. Test of symmetry in nonparametric regression. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 1, pp. 110-130. http://geodesic.mathdoc.fr/item/TVP_2002_47_1_a7/