TY - JOUR

T1 - Universal composite hypothesis testing

T2 - A competitive minimax approach

AU - Feder, Meir

AU - Merhav, Neri

PY - 2002/6

Y1 - 2002/6

N2 - A novel approach is presented for the long-standing problem of Composite hypothesis testing. In composite hypothesis testing, unlike in simple hypothesis testing, the probability function of the observed data, given the hypothesis, is uncertain as it depends on the unknown value of some parameter. The proposed approach is to minimize the worst case ratio between the probability of error of a decision rule that is independent of the unknown parameters and the minimum probability of error attainable given the parameters. The principal solution to this minimax problem is presented and the resulting decision rule is discussed. Since the exact solution is, in general, hard to find, and a fortiori hard to implement, an approximation method that yields an asymptotically minimax decision rule is proposed. Finally, a variety of potential application areas are provided in signal processing and communications with special emphasis on universal decoding.

AB - A novel approach is presented for the long-standing problem of Composite hypothesis testing. In composite hypothesis testing, unlike in simple hypothesis testing, the probability function of the observed data, given the hypothesis, is uncertain as it depends on the unknown value of some parameter. The proposed approach is to minimize the worst case ratio between the probability of error of a decision rule that is independent of the unknown parameters and the minimum probability of error attainable given the parameters. The principal solution to this minimax problem is presented and the resulting decision rule is discussed. Since the exact solution is, in general, hard to find, and a fortiori hard to implement, an approximation method that yields an asymptotically minimax decision rule is proposed. Finally, a variety of potential application areas are provided in signal processing and communications with special emphasis on universal decoding.

KW - Composite hypothesis testing

KW - Error exponents

KW - Generalized likelihood ratio test

KW - Likelihood ratio

KW - Maximum likelihood (ML)

KW - Universal decoding

UR - http://www.scopus.com/inward/record.url?scp=0036612335&partnerID=8YFLogxK

U2 - 10.1109/TIT.2002.1003837

DO - 10.1109/TIT.2002.1003837

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AN - SCOPUS:0036612335

SN - 0018-9448

VL - 48

SP - 1504

EP - 1517

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 6

ER -