Transportation inequalities for hidden Markov chains and applications

被引：2

作者：

Hu ShuLan ^{[1
]}

机构：

[1] Zhongnan Univ Econ & Law, Dept Stat, Wuhan 430073, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 05期

基金：

中央高校基本科研业务费专项资金资助;

关键词：

hidden Markov chains; deviation inequalities; transportation cost-information inequality; measure concentration; exponential forgetting; geometric ergodicity; MAXIMUM-LIKELIHOOD-ESTIMATION; LIMIT-THEOREM; ERGODICITY;

D O I：

10.1007/s11425-011-4178-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove some transportation inequalities for hidden Markov chains, generalize the results proved by Kontorovich and Ramanan in two directions and give some applications to log-likelihood functions and hypothesis testing.

引用

页码：1027 / 1042

页数：16

共 27 条

[1]

[Anonymous], 2001, The Concentration of Measure Phenomenon

[2] ANALYSIS OF AN IDENTIFICATION ALGORITHM ARISING IN THE ADAPTIVE ESTIMATION OF MARKOV-CHAINS [J].

ARAPOSTATHIS, A ;

MARCUS, SI .

MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1990, 3 (01) :1-29

[3] Lyapunov exponents for finite state nonlinear filtering [J].

Atar, R ;

Zeitouni, O .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1997, 35 (01) :36-55

[4]

Bickel PJ, 1998, ANN STAT, V26, P1614

[5]

BOBKOV S, 1982, J FUNCT ANAL, V163, P1

[6]

Bolley F, 2005, ANN FAC SCI TOULOUSE, V14, P331, DOI 10.5802/afst.1095

[7] Transportation cost-information inequalities and applications to random dynamical systems and diffusions [J].

Djellout, H ;

Guillin, A ;

Wu, L .

ANNALS OF PROBABILITY, 2004, 32 (3B) :2702-2732

[8] MAXIMUM-LIKELIHOOD-ESTIMATION AND IDENTIFICATION DIRECTLY FROM SINGLE-CHANNEL RECORDINGS [J].

FREDKIN, DR ;

RICE, JA .

PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, 1992, 249 (1325) :125-132

[9] PRODUCTS OF RANDOM MATRICES [J].

FURSTENBERG, H ;

KESTEN, H .

ANNALS OF MATHEMATICAL STATISTICS, 1960, 31 (02) :457-469

[10] PROBABILITY-INEQUALITIES FOR SUMS OF BOUNDED RANDOM-VARIABLES [J].

HOEFFDING, W .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1963, 58 (301) :13-+

← 1 2 3 →