On Two-stage LAO Testing of Multiple Hypotheses for a Pair of Families of Probability Distributions

摘要

A multiple hypotheses two-stage testing for an object characterized by two separated families of hypothetical probability distributions is considered. We introduce two versions of procedure of multiple hypotheses testing in a pair of stages such that in the first stage we determine one family of distributions and then at the second stage of test we indicate the object’s distribution within the selected family. The matrix of reliabilities (error probability exponents) of logarithmically asymptotically optimal (LAO) hypothesis testing by a pair of stages is investigated and compared with the analogous matrix of one-stage procedure of testing designed in earlier works. Advantages of the two-stage LAO testing are revealed.