bootstrap probability

We define This is the bootstrap probability for y=η(0,v).  The z-value is . This becomes z1[v,tau1]=-zc[0,{0,0,0,0},v,tau1]. For a general y=η(u,v) with u~=0, the expression changes only by the linear term in u and the difference is only

The following w1=tau1 z1[v,tau1] is regarded as another w.

Here we obtain the coefficients cc for w1. The scale tau1 is specified instead of tau.

The distribution function of w1 under v0 and scale tau is  .

We can use the function zq2cc to obtain ccw1 directly from w1[v].

We can do the same as above in another way though zq.

The usual bootstrap probability is defined from   with tau=1. We denote it as . The corresponding z-value is denoted by

The distribution function of is denoted by .

Under v0=0, zfz0 becomes