Sharp large deviations for gaussian quadratic forms with applications
ESAIM: Probability and Statistics, Volume 4 (2000), pp. 1-24.
@article{PS_2000__4__1_0,
author = {Bercu, Bernard and Gamboa, Fabrice and Lavielle, Marc},
title = {Sharp large deviations for gaussian quadratic forms with applications},
journal = {ESAIM: Probability and Statistics},
pages = {1--24},
publisher = {EDP-Sciences},
volume = {4},
year = {2000},
zbl = {0939.60013},
mrnumber = {1749403},
language = {en},
url = {http://www.numdam.org/item/PS_2000__4__1_0/}
}
TY  - JOUR
AU  - Bercu, Bernard
AU  - Gamboa, Fabrice
AU  - Lavielle, Marc
TI  - Sharp large deviations for gaussian quadratic forms with applications
JO  - ESAIM: Probability and Statistics
PY  - 2000
DA  - 2000///
SP  - 1
EP  - 24
VL  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/PS_2000__4__1_0/
UR  - https://zbmath.org/?q=an%3A0939.60013
UR  - https://www.ams.org/mathscinet-getitem?mr=1749403
LA  - en
ID  - PS_2000__4__1_0
ER  - 
%0 Journal Article
%A Bercu, Bernard
%A Gamboa, Fabrice
%A Lavielle, Marc
%T Sharp large deviations for gaussian quadratic forms with applications
%J ESAIM: Probability and Statistics
%D 2000
%P 1-24
%V 4
%I EDP-Sciences
%G en
%F PS_2000__4__1_0
Bercu, Bernard; Gamboa, Fabrice; Lavielle, Marc. Sharp large deviations for gaussian quadratic forms with applications. ESAIM: Probability and Statistics, Volume 4 (2000), pp. 1-24. http://www.numdam.org/item/PS_2000__4__1_0/

[1] Azencott R. and Dacunha-Castelle D., Séries d'observations irrégulières. Masson ( 1984). | MR | Zbl

[2] Bahadur R. and Ranga Rao R., On deviations of the sample mean. Ann. Math. Statist. 31 ( 1960) 1015-1027. | MR | Zbl

[3] Barndoff-Nielsen O.E. and Cox D.R., Asymptotic techniques for uses in statistics. Chapman and Hall, Londres ( 1989). | MR | Zbl

[4] Barone P., Gigli A. and Piccioni M., Optimal importance sampling for some quadratic forms of A.R.M.A. processes. IEEE Trans. Inform. Theory 41 ( 1995) 1834-1844. | MR | Zbl

[5] Basor E., A localization theorem for Toeplitz determinants. Indiana Univ. Math. J. 28 ( 1979) 975-983. | MR | Zbl

[6] Basor E., Asymptotic formulas for Toeplitz and Wiener-Hopf operators. Integral Equations Operator Theory 5 ( 1982) 659-665. | MR | Zbl

[7] Bercu B., Gamboa F. and Rouault A., Large deviations for quadratic forms of stationary Gaussian processes. Stochastic Process. Appl. 71 ( 1997) 75-90. | MR | Zbl

[8] Book S.A., Large deviation probabilities for weighted sums. Ann. Math. Statist. 43 ( 1972) 1221-1234. | MR | Zbl

[9] Bottcher A. and Silbermann. Analysis of Toeplitz operators. Springer, Berlin ( 1990). | MR | Zbl

[10] Bouaziz M., Testing Gaussian sequences and asymptotic inversion of Toeplitz operators. Probab. Math. Statist. 14 ( 1993) 207-222. | MR | Zbl

[11] Bryc W. and Dembo A., Large deviations for quadratic functionals of Gaussian processes. J. Theoret. Probab. 10 ( 1997) 307-332. | MR | Zbl

[12] Bryc W. and Smolenski W., On large deviation principle for a quadratic functional of the autoregressive process. Statist. Probab. Lett. 17 ( 1993) 281-285. | MR | Zbl

[13] Bucklew J.A., Large deviations techniques in decision, simulation, and estimation. Wiley ( 1990). | MR

[14] Bucklew J. and Sadowsky J., A contribution to the theory of Chernoff bounds. IEEE Trans. Inform. Theory 39 ( 1993) 249-254. | MR | Zbl

[15] Coursol J. and Dacunha-Castelle D., Sur la formule de Chernoff pour deux processus gaussiens stationnaires. C. R. Acad. Sci. Sér. I Math. 288 ( 1979) 769-770. | MR | Zbl

[16] Cramér H., Random variables and probability distributions. Cambridge University Press ( 1970). | JFM | MR | Zbl

[17] Dacunha-Castelle D., Remarque sur l'étude asymptotique du rapport de vraisemblance de deux processus gaussiens. C. R. Acad. Sci. Sér. I Math. 288 ( 1979) 225-228. | MR | Zbl

[18] Dembo A. and Zeitouni O., Large deviations techniques and applications. Jones and Barblett Pub. Boston ( 1993). | MR | Zbl

[19] Esseen C., Fourier analysis of distribution functions. Acta Math. 77 ( 1945) 1-25. | MR | Zbl

[20] Gamboa F. and Gassiat E., Sets of superresolution and the maximum entropy method on the mean. SIAM J. Math. Anal. 27 ( 1996) 1129-1152. | MR | Zbl

[21] Gamboa F. and Gassiat E., Bayesian methods for ill posed problems. Ann. Statist. 25 ( 1997) 328-350. | MR | Zbl

[22] Golinskii B. and Ibragimov I., On Szegös limit theorem. Math. USSR- Izv. 5 ( 1971) 421-444. | Zbl

[23] Grenander V. and Szegö G., Toeplitz forms and their applications. University of California Press ( 1958). | MR | Zbl

[24] Guyon X., Random fields on a network/ modeling, statistics and applications. Springer ( 1995). | MR | Zbl

[25] Hartwig R.E. and Fisher M.E., Asymptotic behavior of Toeplitz matrices and determinants. Arch. Rational Mech. Anal. 32 ( 1969) 190-225. | MR | Zbl

[26] Howland J., Trace class Hankel operators. Quart. J. Math. Oxford Ser. (2) 22 ( 1971) 147-159. | MR | Zbl

[27] Jensen J.L., Saddlepoint Approximations. Oxford Statist. Sci. Ser. 16 ( 1995). | MR | Zbl

[28] Johansson K., On Szegös asymptotic formula for Toeplitz determinants and generalizations. Bull. Sci. Math. 112 ( 1988) 257-304. | MR | Zbl

[29] Lavielle M., Detection of changes in the spectrum of a multidimensional process. IEEE Trans. Signal Process. 42 ( 1993) 742-749. | Zbl

[30] Lehmann E.L., Testing statistical hypotheses. John Wiley and Sons, New-York ( 1959). | MR | Zbl

[31] Rudin W., Real and complex analysis. McGraw Hill International Editions ( 1987). | MR | Zbl

[32] Taniguchi M., Higher order asymptotic theory for time series analysis. Springer, Berlin ( 1991). | MR | Zbl

[33] Widom H., On the limit block Toeplitz determinants. Proc. Amer. Math. Soc. 50 ( 1975) 167-173. | MR | Zbl

[34] Widom H., Asymptotic behavior of block Toeplitz matrices and determinants IIAdv. Math. 21 ( 1976). | MR | Zbl