06088188

j

06088188 Ermakov, Mikhail Nonparametric signal detection with small type I and type II error probabilities. Stat. Inference Stoch. Process. 14, No. 1, 1-19 (2011). 2011 Springer, Dordrecht EN signal detection nonparametric hypothesis testing kernel estimator large deviations

doi:10.1007/s11203-010-9048-5

Summary: In the problem of signal detection in the heteroscedastic Gaussian white noise we show asymptotic minimaxity of kernel-based tests. The test statistics equal $L _{2}$-norms of kernel estimators. The sets of alternatives are defined by the sets of all signals such that $L _{2}$- norms of signals smoothed by the kernel exceed some constants ${\rho_\epsilon}$. The constants ${\rho_\epsilon}$ depend on the power ${\epsilon}$ of noise and ${\rho_\epsilon \to 0}$ as ${\epsilon \to 0}$. The setup is considered in the zone of moderate deviation probabilities. We suppose that type I or type II error probabilities of tests tend to zero as ${\epsilon \to 0}$.