Geodesic
Minimax testing of hypotheses on the distribution density for ellipsoids in~$l_p$
Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 530-553

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Let $x_1,\dots,x_N$ be an independent sample with distribution density $f(x)$. A minimax problem of testing a simple hypothesis $f=f_0$ against a complex alternative $f\ne f_\theta$, $\theta\in\Phi_{N,p}^1$, is considered (see Definition in § 1). Asymptotic formulas for error probabilities are obtained which correspond to asymptotic minimax sequences of tests under weaker constraints on the, form of the sets $\Phi_{N,p}^1$ than studied in earlier works.
Keywords: test of hypotheses on the distribution density, complex alternative, minimax approach, asymptotic minimax tests. 
@article{TVP_1994_39_3_a4,
     author = {Yu. I. Ingster},
     title = {Minimax testing of hypotheses on the distribution density for ellipsoids in~$l_p$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {530--553},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a4/}
}
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Yu. I. Ingster. Minimax testing of hypotheses on the distribution density for ellipsoids in~$l_p$. Teoriâ veroâtnostej i ee primeneniâ, Tome 39 (1994) no. 3, pp. 530-553. http://geodesic.mathdoc.fr/item/TVP_1994_39_3_a4/