ABSTRACT
L(θ;Y1, . . . , Yn) = nY i=1
fθ (Yi) ,
and accept H0 otherwise, where kα = kα (n,α,θ0,θ1) is determined by
Prθ0 (hn ≥ kα) = α,
where α (0 < α < 1) is the significance level.
0 0 1 0 uniformly most powerful test does not exist and we have to rely on other criteria for
the choice of an appropriate test statistic. In such situations the classical solutions are
Wald test statistic, Rao test statistic, likelihood ratio test statistic and more recently the
test statistics based on φ-divergence measures: φ-divergence test statistics. The same problem appears with composite null hypotheses of the type H0 : θ ∈ Θ0 ⊂ Θ and again the previous test statistics provide good solutions. In this chapter we study the
properties of φ-divergence test statistics for testing simple and composite null hypotheses.
