Empirical Analogues of Statistical Tests with Guaranteed Conclusions

Methods of kernel estimation of a priori density in the deconvolution problem are used to construct guaranteed procedures for distinguishing between two one-sided hypotheses. The situation is considered when the observed random variable is the sum of an unknown parameter and a centered normal error with a known variance. Consistent empirical estimates are constructed for the d-posterior risk function. The convergence of the corresponding critical constant to the optimal value is established. The accuracy of the procedures is illustrated numerically on three variants of the prior distribution.