TY - GEN
T1 - Pseudo-regenerative block-bootstrap for hidden Markov chains
AU - Clémençon, S.
AU - Garivier, A.
AU - Tressou, J.
PY - 2009/12/25
Y1 - 2009/12/25
N2 - This paper is devoted to extend the regenerative block-bootstrap (RBB) proposed in [1] for regenerative Markov chains to Hidden Markov Models {(X n, Y n)} n∈ℕ. In the HMM setup, regeneration times of the underlying chain X (i.e. consecutive times at which it visits a given state), which are regeneration times for the bivariate chain (X, Y) as well, are not observable. The principle underlying the RBB extension consists in resampling the output by generating first a sequence of approximate regeneration times for X from data Y (n) = (Y 1, ⋯, Y n), by splitting up next Y (n) into data blocks corresponding to the pseudo-renewal times obtained and, eventually, by resampling the blocks until the (random) length of the reconstructed series is a least n. Beyond the algorithmic description of the resampling procedure, which we call "hidden regenerative block-bootstrap" (HRBB), its performance is evaluated on a simple simulation example.
AB - This paper is devoted to extend the regenerative block-bootstrap (RBB) proposed in [1] for regenerative Markov chains to Hidden Markov Models {(X n, Y n)} n∈ℕ. In the HMM setup, regeneration times of the underlying chain X (i.e. consecutive times at which it visits a given state), which are regeneration times for the bivariate chain (X, Y) as well, are not observable. The principle underlying the RBB extension consists in resampling the output by generating first a sequence of approximate regeneration times for X from data Y (n) = (Y 1, ⋯, Y n), by splitting up next Y (n) into data blocks corresponding to the pseudo-renewal times obtained and, eventually, by resampling the blocks until the (random) length of the reconstructed series is a least n. Beyond the algorithmic description of the resampling procedure, which we call "hidden regenerative block-bootstrap" (HRBB), its performance is evaluated on a simple simulation example.
KW - Bootstrap
KW - Confidence interval
KW - Hidden Markov chain
KW - Regeneration
KW - Resampling
UR - https://www.scopus.com/pages/publications/72349087790
U2 - 10.1109/SSP.2009.5278537
DO - 10.1109/SSP.2009.5278537
M3 - Conference contribution
AN - SCOPUS:72349087790
SN - 9781424427109
T3 - IEEE Workshop on Statistical Signal Processing Proceedings
SP - 465
EP - 468
BT - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
T2 - 2009 IEEE/SP 15th Workshop on Statistical Signal Processing, SSP '09
Y2 - 31 August 2009 through 3 September 2009
ER -