Nothing
rec3 <- function(Q,yv,PI,Pio,pim){
# preliminaries
out = dim(Pio)
ns = out[1]; k = out[2]; TT = out[3]
# for t=T
if(k==1){
U = array(1,c(k,ns,TT)); V = matrix(ns*(TT-1),k,k)
}else{
U = array(0,c(k,ns,TT)); V = matrix(0,k,k)
U[,,TT] = t((yv*Q[,,TT])/pim)
Q1 = t((yv*Q[,,TT-1])/pim)
P1 = Pio[,,TT]
R = matrix(1,k,ns);
for(i in 1:ns) V = V+Q1[,i]%o%P1[i,]
# for other t
## Se TT = 2
if(TT>2){
for(t in seq(TT-1,2,-1)){
R = PI%*%(t(Pio[,,t+1])*R)
P1 = Pio[,,t]*t(R)
U[,,t] = Q1*R
Q1 = t((yv*Q[,,t-1])/pim)
for(i in 1:ns) V = V+Q1[,i]%o%P1[i,]
}
}
V = PI*V
R = PI%*%(t(Pio[,,2])*R)
U[,,1] = Q1*R
}
out = list(U=U,V=V)
out
}
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