TY - GEN
T1 - Estimating a gaussian random walk first-passage time from noisy or delayed observations
AU - Burnashev, Marat
AU - Tchamkerten, Aslan
PY - 2011/1/1
Y1 - 2011/1/1
N2 - Given a Gaussian random walk X with drift, we consider estimating its first-passage time , of a given level l, with a stopping time defined over an observation process Y that is either a noisy version of X, or a delayed version of X. For both cases, we provide lower bounds on average moments E|ν-T p, p≥ 1, for any stopping rule ν , and exhibit simple stopping rules that achieve these bounds in the large threshold regime and in the large threshold large delay regime, respectively. The results immediately extend to the corresponding continuous time settings where X and Y are standard Wiener processes with drift.
AB - Given a Gaussian random walk X with drift, we consider estimating its first-passage time , of a given level l, with a stopping time defined over an observation process Y that is either a noisy version of X, or a delayed version of X. For both cases, we provide lower bounds on average moments E|ν-T p, p≥ 1, for any stopping rule ν , and exhibit simple stopping rules that achieve these bounds in the large threshold regime and in the large threshold large delay regime, respectively. The results immediately extend to the corresponding continuous time settings where X and Y are standard Wiener processes with drift.
KW - Estimation
KW - Hypothesis Testingz
KW - Optimal Stopping Theory
KW - Stopping Times
U2 - 10.1109/ISIT.2011.6033813
DO - 10.1109/ISIT.2011.6033813
M3 - Conference contribution
AN - SCOPUS:80054811480
SN - 9781457705953
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1594
EP - 1597
BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2011 IEEE International Symposium on Information Theory, ISIT 2011
Y2 - 31 July 2011 through 5 August 2011
ER -