ABSTRACT
In the previous chapter we have studied the family of φ-divergence test statistics, Tφn (bp,p0), for the problem of goodness-of-fit. If we denote by FTφn (bp,p0)(t) the exact distribution of Tφn (bp,p0), for fixed φ, we established that
F Tφn (bp,p0)(t) = Fχ2M−1 (t) + o (1) as n→∞, (4.1)
under the null hypothesis
H0 : p = p 0. (4.2)
Based on (4.1) we considered for the problem of goodness-of-fit given in (4.2) the
decision rule
“Reject, with significance level α, H0 if Tφn (bp,p0) > χ2M−1,α”. (4.3) Now in this chapter we shall present some criteria to choose the best function φ in some sense. In Section 4.2, Pitman asymptotic efficiency (contiguous alternative hypotheses), Bahadur efficiency and some asymptotic approximations of the power function for the φ-divergence test statistic are studied.
