### linearly interpolate est'ed coefs:
### W.P. 4/5/08

##Input: at Ts[i], betas[i, ] give the coef's
##Goal: for each fracs[i], linearly interpolate betas at fracs[i].
linapprox<-function(betas, Ts0, fracs){
p<-ncol(betas); n<-nrow(betas)
betas0<-matrix(0, nrow=length(fracs), ncol=p)
for(j in 1:p)
  betas0[,j]<-approx(Ts0, betas[, j], fracs)$y
betas0
}