Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies
Yuri I. Ingster; Irina A. Suslina
ESAIM: Probability and Statistics (2000)
- Volume: 4, page 53-135
- ISSN: 1292-8100
Access Full Article
topHow to cite
topIngster, Yuri I., and Suslina, Irina A.. "Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies." ESAIM: Probability and Statistics 4 (2000): 53-135. <http://eudml.org/doc/104267>.
@article{Ingster2000,
author = {Ingster, Yuri I., Suslina, Irina A.},
journal = {ESAIM: Probability and Statistics},
keywords = {asymptotics of error probabilities},
language = {eng},
pages = {53-135},
publisher = {EDP Sciences},
title = {Minimax nonparametric hypothesis testing for ellipsoids and Besov bodies},
url = {http://eudml.org/doc/104267},
volume = {4},
year = {2000},
}
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
PB - EDP Sciences
VL - 4
SP - 53
EP - 135
LA - eng
KW - asymptotics of error probabilities
UR - http://eudml.org/doc/104267
ER -
References
top- [1] M.V. Burnashev, On the minimax detection of an inaccurately known signal in a Gaussian noise background. Theory Probab. Appl. 24 ( 1979) 107-119. Zbl0433.60043MR522240
- [2] A. Cohen, I. Daubechies, B. Jewerth and P. Vial, Multiresolution analysis, wavelets and fast algorithms on an interval. C. R. Acad. Sci. Paris (A) 316 ( 1993) 417-421. Zbl0768.42015MR1209259
- [3] A. Cohen, I. Daubechies and P. Vial, Wavelets on an interval and fast wavelet transforms. Appl. Comput. Harmon. Anal 1 ( 1993) 54-81. Zbl0795.42018MR1256527
- [4] D.L. Donoho and I.M. Johnstone, Minimax estimation via wavelet shrinkage. Technical Report 402 Dep. of Statistics, Stanford University ( 1992). Zbl0935.62041
- [5] D.L. Donoho, I.M. Johnstone, G. Kerkyacharian and D. Picard, Wavelet shrinkage: Asymptopia? J. Roy. Statist. Soc. 57 ( 1995) 301-369. Zbl0827.62035MR1323344
- [6] M.S. Ermakov, Minimax detection of a signal in a Gaussian white noise. Theory Probab. Appl. 35 ( 1990) 667-679. Zbl0744.62117MR1090496
- [7] I.A. Ibragimov and R.Z. Khasminskii, One problem of statistical estimation in a white Gaussian noise. Soviet Math. Dokl. 236 ( 1977) 1351-1354. Zbl0389.62024
- [8] I.A. Ibragimov and R.Z. Khasminskii, Statistical Estimation: Asymptotic Theory. Springer, Berlin-New York ( 1981). Zbl0467.62026MR620321
- [9] Yu.I. Ingster, Minimax nonparametric detection of signals in white Gaussian noise. Problems Inform. Transmission 18 ( 1982) 130-140. Zbl0499.94002MR689340
- [10] Yu.I. Ingster, Minimax testing of nonparametric hypotheses on a distribution density in Lp-metrics. Theory Probab. Appl. 31 ( 1986) 333-337. Zbl0629.62049
- [11] Yu.I. Ingster, 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]. Zbl0738.94005MR1098696
- [12] Yu.I. Ingster, Asymptotically minimax hypothesis testing for nonparametric alternatives. I, II, III. Math. Methods Statist. 2 ( 1993) 85-114, 171-189, 249-268. Zbl0798.62059MR1257978
- [13] Yu.I. Ingster, 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). Zbl0935.62054MR1449855
- [14] Yu.I. Ingster, Some problems of hypothesis testing leading to infinitely divisible distributions. Math. Methods Statist. 6 ( 1997) 47-69. Zbl0878.62005MR1456646
- [15] Yu.I. Ingster, Adaptation in Minimax Nonparametric Hypothesis Testing for ellipsoids and Besov bodies. Technical Report 419, Weierstrass Institute, Berlin ( 1998).
- [16] Yu.I. Ingster and I.A. Suslina, Minimax signal detection for Besov balls and bodies. Problems Inform. Transmission 34 ( 1998) 56-68. Zbl1113.94303MR1654822
- [17] O.V. Lepski, On asymptotical exact testing of nonparametric hypotheses. CORE D.P. 9329, Université Catholique de Louvain ( 1993).
- [18] O.V. Lepski, E. Mammen and V.G. Spokoiny, Optimal spatial adaptation to ingomogeneous smoothness: An approach based on kernal estimates with variable bandwidth selectors. Ann. Statist. 25 ( 1997) 929-947. Zbl0885.62044MR1447734
- [19] O.V. Lepski and V.G. Spokoiny, Minimax nonparametric hypothesis testing: the case of an inhomogeneous alternative. Bernoulli 5 ( 1999) 333-358. Zbl0946.62050MR1681702
- [20] O.V. Lepski and A.B. Tsybakov, 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). Zbl0971.62022
- [21] Y. Meyer, Ondlettes. Herrmann, Paris ( 1990).
- [22] M.S. Pinsker, Optimal filtration of square-integrable signals in Gaussian noise. Problems Inform. Transmission 16 ( 1980) 120-133. Zbl0452.94003MR624591
- [23] M. Sion, On general minimax theorems. Pacific J. Math. 58 ( 1958) 171-176. Zbl0081.11502MR97026
- [24] V.G. Spokoiny, Adaptive hypothesis testing using wavelets. Ann. Stat. 24 ( 1996) 2477-2498. Zbl0898.62056MR1425962
- [25] V.G. Spokoiny, Adaptive and spatially adaptive testing of nonparametric hypothesis. Math. Methods Statist. 7 ( 1998) 245-273. Zbl1103.62345MR1651777
- [26] I.A. Suslina, 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). Zbl0819.94014
- [27] I.A. Suslina, 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).
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.