TY - JOUR

T1 - Opportunistic detection rules

T2 - Finite and asymptotic analysis

AU - Zhang, Wenyi

AU - Moustakides, George V.

AU - Poor, H. Vincent

N1 - Funding Information:
W. Zhang was supported in part by the National Natural Science Foundation of China under Grant 61379003, in part by the National Basic Research Program of China (973 Program) under Grant 2012CB316004, and in part by the SRFDP-RGC ERG Joint Research Scheme through the Specialized Research Fund under Grant 20133402140001. H. V. Poor was supported by the U.S. National Science Foundation under Grant DMS-1118605 and Grant ECCS-1343210.
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2016/4

Y1 - 2016/4

N2 - Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed samples. From a sequential decision perspective, ODRs are also mixtures of one-sided and truncated sequential detection rules. Several results regarding ODRs are established in this paper. In the finite regime, the maximum sample size is modeled either as a fixed finite number, or a geometric random variable with a fixed finite mean. For both cases, the corresponding Bayesian formulations are investigated. The former case is a slight variation of the well-known finite-length sequential hypothesis testing procedure in the literature, whereas the latter case is new, for which the Bayesian optimal ODR is shown to be a sequence of likelihood ratio threshold tests with two different thresholds. A running threshold, which is determined by solving a stationary state equation, is used when future samples are still available, and a terminal threshold (simply the ratio between the priors scaled by costs) is used when the statistician reaches the final sample and, thus, has to make a decision immediately. In the asymptotic regime, the tradeoff among the exponents of the (false alarm and miss) error probabilities and the normalized expected stopping time under the alternative hypothesis is completely characterized and proved to be tight, via an information-theoretic argument. Within the tradeoff region, one noteworthy fact is that the performance of the Stein-Chernoff lemma is attainable by ODRs.

AB - Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed samples. From a sequential decision perspective, ODRs are also mixtures of one-sided and truncated sequential detection rules. Several results regarding ODRs are established in this paper. In the finite regime, the maximum sample size is modeled either as a fixed finite number, or a geometric random variable with a fixed finite mean. For both cases, the corresponding Bayesian formulations are investigated. The former case is a slight variation of the well-known finite-length sequential hypothesis testing procedure in the literature, whereas the latter case is new, for which the Bayesian optimal ODR is shown to be a sequence of likelihood ratio threshold tests with two different thresholds. A running threshold, which is determined by solving a stationary state equation, is used when future samples are still available, and a terminal threshold (simply the ratio between the priors scaled by costs) is used when the statistician reaches the final sample and, thus, has to make a decision immediately. In the asymptotic regime, the tradeoff among the exponents of the (false alarm and miss) error probabilities and the normalized expected stopping time under the alternative hypothesis is completely characterized and proved to be tight, via an information-theoretic argument. Within the tradeoff region, one noteworthy fact is that the performance of the Stein-Chernoff lemma is attainable by ODRs.

KW - Chernoff information

KW - Stein- Chernoff Lemma

KW - error exponent

KW - fixedsample- size (FSS) hypothesis testing

KW - opportunistic detection rule (ODR)

KW - optimal stopping,

KW - sequential hypothesis testing

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U2 - 10.1109/TIT.2016.2530087

DO - 10.1109/TIT.2016.2530087

M3 - Article

AN - SCOPUS:84963799516

SN - 0018-9448

VL - 62

SP - 2140

EP - 2152

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 4

M1 - 7407388

ER -