Deviation Inequalities for the Estimator of Linear Parameter in Stochastic Processes

References

• Akahira , M. , Takeuchi , K. ( 1981 ). Asymptotic Efficiency of Statistical Estimators . New York : Springer-Verlag .
   Google Scholar
• Crowder , M. ( 1986 ). On consistency and inconsistency of estimating equations . Econometric Theor. 2 : 305 – 330 .
   Google Scholar
• de la Peña , V. H . ( 1999 ). A general class of exponential inequalities for martingales and ratios . Ann. Probab. 27 : 537 – 564 .
   Web of Science ®Google Scholar
• Dembo , A. , Zeitouni , O. ( 1998 ). Large Deviations Techniques and Applications. , 2nd ed. New York : Springer-Verlag .
   Google Scholar
• Djellout , H. , Guillin , A. , Wu , L. M. ( 2006 ). Moderate deviations of empirical periodogram and non-linear functionals of moving average processes . Ann. Inst. H. Poincaré Probab. Statist. 42 : 393 – 416 .
   Google Scholar
• Gao , F. Q. ( 2001 ). Moderate deviations for the maximum likelihood estimator . Statist. Probab. Lett. 55 : 345 – 352 .
   Web of Science ®Google Scholar
• Godambe , V. F. ( 1985 ). The foundations of finite sample estimation in stochastic processes . Biometrika 72 : 419 – 428 .
   Web of Science ®Google Scholar
• Ibragimov , I. A. , Has'miniskii , R. Z. ( 1979 ). Statistical Estimation . New York : Springer-Verlag .
   Google Scholar
• Ibragimov , I. , Radavicius , M. ( 1981 ). Probability of large deviations for the maximum likelihood estimator . Soviet Math. Dokl. 23 ( 2 ): 403 – 406 .
   Google Scholar
• Liptser , R. , Spokoiny , V. ( 2000 ). Deviation probability bound for martingales with applications to statistical estimation . Statist. Probab. Lett. 46 ( 4 ): 347 – 357 .
   Web of Science ®Google Scholar
• Miao , Y. (2005). Lower bound of moderate deviation for the Bayesian estimator. J. Math. (PRC) 25(4):358–360.
   Google Scholar
• Miao , Y. ( 2006 ). A note on the martingale inequality . JIPAM. J. Inequal. Pure Appl. Math. 7 ( 5 ), Art. 187 .
   Google Scholar
• Miao , Y. ( 2008 ). Concentration inequalities for semi-bounded martingales . ESAIM Probab. Statist. 12 : 51 – 57 .
   Google Scholar
• Miao , Y. , Shen , S. ( 2007 ). Moderate deviation principle for autoregressive processes. Submitted .
   Google Scholar
• Puhalskii , A. , Spokoiny , V. ( 1998 ). On large-deviation efficiency in statistical inference . Bernoulli 4 ( 2 ): 203 – 272 .
   Web of Science ®Google Scholar
• Ruskeepää , H. ( 1991 ), A note on estimating equations for linear parameters in discrete-time stochastic processes . Statistics 22 ( 3 ): 403 – 408 .
   Google Scholar
• Thavaneswaran , A. , Thompson , M. E. ( 1986 ). Optimal estimation for semi-martingales . J. Appl. Probab. 23 : 409 – 417 .
   Web of Science ®Google Scholar
• Wu , L. M. ( 1997 ). An introduction to large deviations (in Chinese) . In: Yan , J. A. , Peng , S. G. , Fang , S. Z. , Wu , L. M. , eds. Several Topics in Stochastic Analysis . Beijing : Press of Sciences of China , pp. 225 – 336 .
   Google Scholar