NORMAL APPROXIMATION FOR FUNCTIONS OF HIDDEN MARKOV MODELS

被引：1

作者：

Houdre, Christian ^{[1
]}

Kerchev, George ^{[2
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Univ Luxembourg, Unite Rech Math, Maison 6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg

来源：

ADVANCES IN APPLIED PROBABILITY | 2022年 / 54卷 / 02期

关键词：

Stein?s method; Markov chains; generalized perturbative approach; normal approximation; stochastic geometry; LONGEST COMMON SUBSEQUENCES; LENGTH;

D O I：

10.1017/apr.2021.40

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The generalized perturbative approach is an all-purpose variant of Stein???s method used to obtain rates of normal approximation. Originally developed for functions of independent random variables, this method is here extended to functions of the realization of a hidden Markov model. In this dependent setting, rates of convergence are provided in some applications, leading, in each instance, to an extra log-factor vis-??-vis the rate in the independent case.

引用

页码：536 / 569

页数：34

共 50 条

[1] Approximation of stationary processes by hidden Markov models
Lorenzo Finesso
Angela Grassi
Peter Spreij
[J]. Mathematics of Control, Signals, and Systems, 2010, 22 : 1 - 22
[2] On approximation of smoothing probabilities for hidden Markov models
Lember, Jueri
[J]. STATISTICS & PROBABILITY LETTERS, 2011, 81 (02) : 310 - 316
[3] Estimation and strong approximation of hidden Markov models
Gerencsér, L
Molnár-Sáska, G
[J]. POSITIVE SYSTEMS, PROCEEDINGS, 2003, 294 : 313 - 320
[4] Approximation of stationary processes by hidden Markov models
Finesso, Lorenzo
Grassi, Angela
Spreij, Peter
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2010, 22 (01) : 1 - 22
[5] A correction on approximation of smoothing probabilities for hidden Markov models
Lember, Jueri
[J]. STATISTICS & PROBABILITY LETTERS, 2011, 81 (09) : 1463 - 1464
[6] Multiscale stochastic approximation for parametric optimization of hidden Markov models
Bhatnagar, S
Borkar, VS
[J]. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 1997, 11 (04) : 509 - 522
[7] On Maximum A Posteriori Approximation of Hidden Markov Models for Proportional Data
Ali, Samr
Bouguila, Nizar
[J]. 2020 IEEE 22ND INTERNATIONAL WORKSHOP ON MULTIMEDIA SIGNAL PROCESSING (MMSP), 2020,
[8] Markov models - hidden Markov models
Grewal, Jasleen K.
Krzywinski, Martin
Altman, Naomi
[J]. NATURE METHODS, 2019, 16 (09) : 795 - 796
[9] Markov models — hidden Markov models
Jasleen K. Grewal
Martin Krzywinski
Naomi Altman
[J]. Nature Methods, 2019, 16 : 795 - 796
[10] Consistent and asymptotically normal parameter estimates for hidden Markov mixtures of Markov models
Vandekerkhove, P
[J]. BERNOULLI, 2005, 11 (01) : 103 - 129

← 1 2 3 4 5 →