No-decision region in tests with frequentists conditional and bayesian
interpretation

Carla Regina Guimarães BRIGHENTI[1]^{}

Lucas Monteiro CHAVES [2]^{}

§ ABSTRACT: The Bayesian Test is a Likelihood
Ratio Test with critical values given by product of the ratio between prior
densities and the ratio between losses. In this way, for some determined values
of ρ and l there
are coincident critics regions for a bayesian test and for a conditional
frequentist test. The evidence measure reported in the bayesian test is the
posterior probability while the conditional test is the conditional error
probability (CEP). Depending on the conditioning statistic used and the ρ and l values, these values can be
numerically the same, defining a “unified” test. But when the prior probability
or the CEP are numerically the same and superior to 1/2, it must be
incorporated a “no-decision region”, NDR. The NDR construction depends on the
partitioning function H(x) of the conditional test and the p and l values. In
this work, it was studied size of the NDR to hypothesis test of the parameter
Exponential distribution with samples of different sizes. It was concluded that
the size of the NDR depends on the size of the sample and that some situations
can make the test unified inadequate.

§ KEYWORDS: Conditional error
probability; no-decision region; partitioning function; posterior probability.