Abstract
This chapter is devoted to somme applications of concentration inequalities in probability and statistics. The first one deals with parameter estimation for autoregressive process and the second one is an improvement of a recent result on random permutations. The third one is a new result on empirical periodogram and the last one deals with random matrices.
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References
Anderson, G. W., Guionnet A. and Zeitouni, O.: An introduction to random matrices. Cambridge University Press, New York, (2010)
Bai, Z. and Silverstein, J. W.: Spectral analysis of large dimensional random matrices. Springer Series in Statistics. Springer, New York, second edition, (2009)
Bercu, B., Gamboa, F. and Rouault, A.: Large deviations for quadratic forms of stationary Gaussian processes. Stochastic Process. Appl. 71 75–90 (1997)
Bercu, B. and Touati, A.: Exponential inequalities for self-normalized martingales with applications. Ann. Appl. Probab. 18 1848–1869 (2008)
Bercu, B., Bony, J. F. and Bruneau, V.: Large deviations for Gaussian stationary processes and semi-classical analysis, Séminaire de Probabilités 44, Lecture Notes in Mathematics 2046, 409–428 (2012).
Brockwell, P. J. and Davis, R. A.: Time series: Theory and methods. Springer Series in Statistics. Springer, New York, second edition, (2009)
Chatterjee, S.: Stein’s method for concentration inequalities. Probab. Theory Related Fields 138 305–321 (2007)
Dacunha-Castelle, D. and Duflo, M.: Probability and Statistics. Volume II. Springer-Verlag, New York, (1986)
Del Moral, P. and Rio, E.: Concentration inequalities for mean field particle models. Ann. Appl. Probab. 21, 1017–1052 (2011)
Delyon, B.: Concentration inequalities for the spectral measure of random matrices. Electron. Commun. Probab. 15, 549–561 (2010)
Guionnet, A. and Zeitouni, O.: Concentration of the spectral measure for large matrices. Electron. Commun. Probab. 5, 119–136 (2000)
Guntuboyina, A. and Leeb, H.: Concentration of the spectral measure of large Wishart matrices with dependent entries. Electron. Commun. Probab. 14, 334–342 (2009)
Hoeffding, W.: A Combinatorial central limit theorem. Ann. Math. Stat. 22 558–566 (1951)
Laurent, B. and Massart, P.: Adaptive estimation of a quadratic functional by model selection. Ann. Stat. 28 1302–1338 (2001)
Liptser, R. and Spokoiny, V.: Deviation probability bound for martingales with applications to statistical estimation. Statist. Probab. Lett. 46 347–357 (2000)
Worms, J.: Moderate deviations for stable Markov chains and regression models. Electron. J. Probab. 4 1–28 (1999)
Worms, J.: Large and moderate deviations upper bounds for the Gaussian autoregressive process. Statist. Probab. Lett. 51 235–243 (2001)
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Bercu, B., Delyon, B., Rio, E. (2015). Applications in probability and statistics. In: Concentration Inequalities for Sums and Martingales. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-22099-4_4
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DOI: https://doi.org/10.1007/978-3-319-22099-4_4
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