Moderate deviations and hypothesis testing for signal detection problem  

作　　者：GAO FuQing ZHAO ShouJiang 

机构地区：[1]School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China [2]School of Science,China Three Gorges University,Yichang 443002,China

出　　处：《Science China Mathematics》2012年第11期2273-2284,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10871153 and 11171262);the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200804860048)

摘　　要：Abstract We use moderate deviations to study the signal detection problem for a diffusion model. We establish a moderate deviation principle for the log-likelihood function of the diffusion model. Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-ατ（T）, where α〉 0, τ（T） = o（T） and τ（T）→∞ as the observation time T goes to infinity.We use moderate deviations to study the signal detection problem for a diffusion model.We establish a moderate deviation principle for the log-likelihood function of the diffusion model.Then applying the moderate deviation estimates to hypothesis testing for signal detection problem we give a decision region such that its error probability of the second kind tends to zero with faster speed than the error probability of the first kind when the error probability of the first kind is approximated by e-αr(T),where α>0,r(T)=o(T) and r(T) →∞ as the observation time T goes to infinity.

关 键 词：large deviations moderate deviations signal detection hypothesis testing 

分 类 号：O212.1[理学—概率论与数理统计] TN911.23[理学—数学]