@article{PS_2000__4__53_0,
author = {Ingster, Yuri I. and Suslina, Irina A.},
title = {Minimax nonparametric hypothesis testing for ellipsoids and {Besov} bodies},
journal = {ESAIM: Probability and Statistics},
pages = {53--135},
year = {2000},
publisher = {EDP Sciences},
volume = {4},
mrnumber = {1784903},
zbl = {1110.62321},
language = {en},
url = {https://www.numdam.org/item/PS_2000__4__53_0/}
}
TY - JOUR AU - Ingster, Yuri I. AU - Suslina, Irina A. TI - Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies JO - ESAIM: Probability and Statistics PY - 2000 SP - 53 EP - 135 VL - 4 PB - EDP Sciences UR - https://www.numdam.org/item/PS_2000__4__53_0/ LA - en ID - PS_2000__4__53_0 ER -
Ingster, Yuri I.; Suslina, Irina A. Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies. ESAIM: Probability and Statistics, Tome 4 (2000), pp. 53-135. https://www.numdam.org/item/PS_2000__4__53_0/
[1] , On the minimax detection of an inaccurately known signal in a Gaussian noise background. Theory Probab. Appl. 24 ( 1979) 107-119. | Zbl | MR
[2] , , and , Multiresolution analysis, wavelets and fast algorithms on an interval. C. R. Acad. Sci. Paris (A) 316 ( 1993) 417-421. | Zbl | MR
[3] , and , Wavelets on an interval and fast wavelet transforms. Appl. Comput. Harmon. Anal 1 ( 1993) 54-81. | Zbl | MR
[4] and , Minimax estimation via wavelet shrinkage. Technical Report 402 Dep. of Statistics, Stanford University ( 1992).
[5] , , and , Wavelet shrinkage: Asymptopia? J. Roy. Statist. Soc. 57 ( 1995) 301-369. | Zbl | MR
[6] , Minimax detection of a signal in a Gaussian white noise. Theory Probab. Appl. 35 ( 1990) 667-679. | Zbl | MR
[7] and , One problem of statistical estimation in a white Gaussian noise. Soviet Math. Dokl. 236 ( 1977) 1351-1354. | Zbl
[8] and , Statistical Estimation: Asymptotic Theory. Springer, Berlin-New York ( 1981). | Zbl | MR
[9] , Minimax nonparametric detection of signals in white Gaussian noise. Problems Inform. Transmission 18 ( 1982) 130-140. | Zbl | MR
[10] , Minimax testing of nonparametric hypotheses on a distribution density in Lp-metrics. Theory Probab. Appl. 31 ( 1986) 333-337. | Zbl
[11] , Minimax detection of a signals in lp-metrics. Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 184 ( 1990) 152-168 [in Russian, Transl: J. Soviet. Math. 68 ( 1994) 4]. | Zbl | MR
[12] , Asymptotically minimax hypothesis testing for nonparametric alternatives. I, II, III. Math. Methods Statist. 2 ( 1993) 85-114, 171-189, 249-268. | Zbl | MR
[13] , Minimax hypotheses testing for nondegenerate loss functions and extreme convex problems. Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 228 ( 1996) 162-188 (in Russian). | Zbl | MR
[14] , Some problems of hypothesis testing leading to infinitely divisible distributions. Math. Methods Statist. 6 ( 1997) 47-69. | Zbl | MR
[15] , Adaptation in Minimax Nonparametric Hypothesis Testing for ellipsoids and Besov bodies. Technical Report 419, Weierstrass Institute, Berlin ( 1998).
[16] and , Minimax signal detection for Besov balls and bodies. Problems Inform. Transmission 34 ( 1998) 56-68. | Zbl | MR
[17] , On asymptotical exact testing of nonparametric hypotheses. CORE D.P. 9329, Université Catholique de Louvain ( 1993).
[18] , and , Optimal spatial adaptation to ingomogeneous smoothness: An approach based on kernal estimates with variable bandwidth selectors. Ann. Statist. 25 ( 1997) 929-947. | Zbl | MR
[19] and , Minimax nonparametric hypothesis testing: the case of an inhomogeneous alternative. Bernoulli 5 ( 1999) 333-358. | Zbl | MR
[20] and , Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point. Discussion Paper 91, Humboldt-Univ., Berlin. Probab. Theory Related Fields (to be published). | Zbl
[21] , Ondlettes. Herrmann, Paris ( 1990).
[22] , Optimal filtration of square-integrable signals in Gaussian noise. Problems Inform. Transmission 16 ( 1980) 120-133. | Zbl | MR
[23] , On general minimax theorems. Pacific J. Math. 58 ( 1958) 171-176. | Zbl | MR
[24] , Adaptive hypothesis testing using wavelets. Ann. Stat. 24 ( 1996) 2477-2498. | Zbl | MR
[25] , Adaptive and spatially adaptive testing of nonparametric hypothesis. Math. Methods Statist. 7 ( 1998) 245-273. | Zbl | MR
[26] , Minimax detection of a signal for lq-ellipsoids with a removed lp-ball. Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 207 ( 1993) 127-137 (in Russian). | Zbl
[27] , Extreme problems arising in minimax detection of a signal for lq-ellipsoids with a removed lp-ball. Zap. Nauchn. Sem. S.-Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 228 ( 1996312-332 (in Russian).






