TY - GEN

T1 - Strong large deviations for Rao test score and GLRT in exponential families

AU - Moulin, Pierre

AU - Johnstone, Patrick R.

PY - 2015/9/28

Y1 - 2015/9/28

N2 - Exact asymptotics are derived for composite hypothesis testing between two product probability measures Pn vs Qn, subject to a type-I error-probability constraint ϵ. Here P is known but Q is an unknown element of a given d-dimensional regular exponential family. We study the Rao score test, which is a quadratic approximation to the GLRT. The type-II error probability is shown to vanish as equation where D and V are respectively the Kullback-Leibler divergence and the variance of information divergence between P and Q; τ(ϵ; d) is the 1 - ϵ quantile for the χd2 distribution; and the constants βd > 0 and γd are explicitly identified. The asymptotic regret relative to the Neyman-Pearson test (which knows Q) is reflected in the coefficient τ(ϵ; d), as is the cost of dimensionality. Looser asymptotics (with O(1) in place of ϵd) are obtained for the GLRT.

AB - Exact asymptotics are derived for composite hypothesis testing between two product probability measures Pn vs Qn, subject to a type-I error-probability constraint ϵ. Here P is known but Q is an unknown element of a given d-dimensional regular exponential family. We study the Rao score test, which is a quadratic approximation to the GLRT. The type-II error probability is shown to vanish as equation where D and V are respectively the Kullback-Leibler divergence and the variance of information divergence between P and Q; τ(ϵ; d) is the 1 - ϵ quantile for the χd2 distribution; and the constants βd > 0 and γd are explicitly identified. The asymptotic regret relative to the Neyman-Pearson test (which knows Q) is reflected in the coefficient τ(ϵ; d), as is the cost of dimensionality. Looser asymptotics (with O(1) in place of ϵd) are obtained for the GLRT.

UR - http://www.scopus.com/inward/record.url?scp=84969751556&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2015.7282561

DO - 10.1109/ISIT.2015.7282561

M3 - Conference contribution

AN - SCOPUS:84969751556

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 779

EP - 783

BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - IEEE International Symposium on Information Theory, ISIT 2015

Y2 - 14 June 2015 through 19 June 2015

ER -