Minimax nonparametric testing of hypotheses on the distribution density
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 488-512
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Let $X_1,\dots,X_n$ be independent identically distributed random variables having unknown density $f(x)$ in $L_2(\nu)$. The problem consists in testing the hypothesis $f(x)=p(x)$ against the alternative that $f(x)$ belongs to an ellipsoid in $L_2(\nu)$ from which a sphere with center at the point $p(x)$ is removed. To solve the problem we construct an asymptotically minimax sequence of tests. As an example the case where the ellipsoid is a sphere in a Sobolev space is considered.
Keywords:
nonparametric testing of hypotheses, goodness-of-fit test, nonparametric set of alternatives, asymptotically minimax tests, optimal rate of convergence, testing hypotheses about the density of a distribution.
@article{TVP_1994_39_3_a2,
author = {M. S. Ermakov},
title = {Minimax nonparametric testing of hypotheses on the distribution density},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {488--512},
publisher = {mathdoc},
volume = {39},
number = {3},
year = {1994},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a2/}
}
M. S. Ermakov. Minimax nonparametric testing of hypotheses on the distribution density. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 488-512. http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a2/