Power Divergence Statistics.

Cressie and Read (1984) and Read and Cressie (1988) have introduced the power divergence family of test statistics 2Iλ = 2

λ(λ + 1)

ij nij

⎡

⎣



nij mˆ (0)

ij λ

− 1

⎤

⎦, where for λ = −1, 0 the statistics are defined by taking limits. They establish that for any λ, the large sample distribution under H0 is χ2 with the usual degrees of freedom. Show that X2 = 2I1 and G2 = 2I0. Find the relationship between 2I−1/2 and the Freeman-Tukey residuals discussed in Exercise 2.7.7.