Geodesic
On asymptotically efficient statistical inference on a signal parameter
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 70-87 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider the problems of confidence estimation and hypothesis testing on a parameter of signal observed in Gaussian white noise. For these problems we point out lower bounds of asymptotic efficiency in the zone of moderate deviation probabilities. These lower bounds are versions of local asymptotic minimax Hajek–Le Cam lower bound in estimation and the lower bound for Pitman efficiency in hypothesis testing. The lower bounds were obtained for both logarithmic and sharp asymptotics of moderate deviation probabilities. 
@article{ZNSL_2013_420_a3,
     author = {M. S. Ermakov},
     title = {On asymptotically efficient statistical inference on a~signal parameter},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {70--87},
     year = {2013},
     volume = {420},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/}
}
TY  - JOUR
AU  - M. S. Ermakov
TI  - On asymptotically efficient statistical inference on a signal parameter
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2013
SP  - 70
EP  - 87
VL  - 420
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/
LA  - ru
ID  - ZNSL_2013_420_a3
ER  - 
%0 Journal Article
%A M. S. Ermakov
%T On asymptotically efficient statistical inference on a signal parameter
%J Zapiski Nauchnykh Seminarov POMI
%D 2013
%P 70-87
%V 420
%U http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/
%G ru
%F ZNSL_2013_420_a3
M. S. Ermakov. On asymptotically efficient statistical inference on a signal parameter. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 20, Tome 420 (2013), pp. 70-87. http://geodesic.mathdoc.fr/item/ZNSL_2013_420_a3/

[1] J. Hajek, “Local asymptotic minimax and admisibility in estimation”, Proc. Sixth Berkeley Symp. Math. Statist. Probab., v. 1, California Univ. Press, Berkeley, 1972, 175–194 | MR | Zbl

[2] I. A. Ibragimov, R. Z. Khasminskii, Asimptoticheskaya teoriya otsenivaniya, Nauka, Moskva, 1979 | MR

[3] Yu. A. Kutoyants, Identification of Dynamical System with Small Noise, Springer, Berlin, 1994 | MR

[4] L. Le Cam, “Limits of experiments”, Proc. Sixth Berkeley Symp. Math. Statist. Probab., v. 1, California Univ. Press, Berkeley, 1972, 245–261 | MR | Zbl

[5] H. Strasser, Mathematical Theory of Statistics, W. de Gruyter, Berlin, 1985 | MR | Zbl

[6] A. W. van der Vaart, Asymptotic Statistics, Cambridge. University Press, 1998 | MR

[7] R. E. Blahut, “Hypothesis testing and information theory”, IEEE Trans. Inform. Theory, 20 (1974), 405–415 | DOI | MR

[8] R. R. Bahadur, “Asymptotic efficiency of tests and estimates”, Sankhyā, 22 (1960), 229–252 | MR | Zbl

[9] J. Bishwal, Parameter Estimation of Stochastic Differential Equations, Springer, Berlin–Heidelderg, 2008 | MR | Zbl

[10] T. Chiyonobu, “Hypothesis testing for signal detection problem and large deviations”, Nagoya Math. J., 162 (2003), 187–203 | MR

[11] A. Puhalskii, V. Spokoiny, “On large-deviation efficiency in statistical inference”, Bernoulli, 4 (1998), 203–272 | DOI | MR | Zbl

[12] A. A. Borovkov, A. A. Mogulskii, Bolshie ukloneniya i proverka statisticheskikh gipotez, Trudy instituta matematiki SO RAN, 19, Nauka, Novosibirsk, 1992 | MR | Zbl

[13] M. S. Ermakov, “Asimptoticheski effektivnye statisticheskie vyvody dlya veroyatnostei umerennykh uklonenii”, Teoriya veroyatn. i ee primen., 48:4 (2003), 676–700 | DOI | MR | Zbl

[14] M. S. Ermakov, “The sharp lower bound of asymptotic efficiency of estimators in the zone of moderate deviation probabilities”, Electronic J. Statist., 6 (2012), 2150–2184 | DOI | MR | Zbl

[15] M. Radavičius, “From asymptotic efficiency in minimax sense to Bahadur efficiency”, New Trends Probab. Statist., eds. V. Sazonov, T. Shervashidze, VSP/Mokslas, Vilnius, 1991, 629–635 | MR

[16] W. C. M. Kallenberg, “Intermediate efficiency, theory and examples”, Ann. Statist., 11 (1983), 170–182 | DOI | MR | Zbl

[17] M. V. Burnashev, “Ob otsenke maksimalnogo pravdopodobiya parametra signala v belom gaussovskom shume”, Probl. peredachi inform., 11:4 (1975), 55–69 | MR | Zbl

[18] F. Q. Gao, F. J. Zhao, “Moderate deviation and hypothesis testing for signal detection problem”, Sci. China. Math., 55 (2012), 2273–2284 | DOI | MR | Zbl

[19] S. Ihara, Y. Sakuma, “Signal detection in white Gaussian channel”, Proc. Seventh Japan–Russian Symp. Probab. Theory Math. Stat., World Scientific, Singapore, 1996, 147–156 | MR | Zbl

[20] R. S. Liptzer, A. N. Shiriaev, Statistics of Random Processes, Springer, Berlin–Heidelderg, 2005

[21] L. D. Brown, A. V. Carter, M. G. Low, C. H. Zhang, “Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift”, Ann. Statist., 32 (2004), 2074–2097 | DOI | MR | Zbl

[22] G. K. Golubev, M. Nussbaum, H. H. Zhou, “Asymptotic equivalence of spectral density estimation and Gaussian white noise”, Ann. Statist., 38 (2010), 181–214 | DOI | MR | Zbl

[23] J. Wolfowitz, “Asymptotic efficiency of the maximum likelihood estimator”, Teoriya veroyatn. i ee primen., 10:2 (1965), 267–281 | MR | Zbl