two-level bootstrap

The ABC conversion formula of Efron (1987) and DiCiccio and Efron (1992) is

The acceleration constant "ac" is

The z-value of the bootstrap probability around the projection is

Thus the ABC formula, denoted za[v] here, becomes

The coefficients 's are obtained by

The distribution function of za[v]  under tau=1 is Pr{za[V]<=w;v0,1}=Φ[zfzq[w,qqza,v0,1]]

Under v0=0, tau=1, it becomes