/*Example 4.5.1-----Subvector test (one sample) */
proc iml;
x1={70,60,65,50,43,40,80,45,30,40};
x2={75,58,70,55,48,41,78,65,55,50};
x=x1||x2;
n=10;p=2; s=1;t=1; f=n-1;
mu0={50 50}; alpha=0.05;
xb=J(n,1,1)*J(1,n,1/n)*x;
ss=(x-xb)`*(x-xb)/(n-1);
Tpsq=n*(xb[1,]-mu0)*inv(ss)*(xb[1,]-mu0)`;
Tssq=n*(xb[1,1]-50)*inv(ss[1,1])*(xb[1,1]-50);
F0=(f-p+1)/t*(Tpsq-Tssq)/(f+Tssq);
Fa=finv(1-0.05,t,f-p+1);
print F0 Fa;
if F0>Fa then print "F0 > Fa:  reject";
         else print "F0 < Fa:  reject";
casq=t/(f-p+1)*Fa;
s21=ss[2,2]-ss[1,2]**2*inv(ss[1,1]);
tt=1/(f-s)*tinv(1-alpha/2, f-s)**2;
if tt<casq then c=tt; else c=casq;
low=xb[1,2]-ss[1,2]*inv(ss[1,1])*(xb[1,1]-mu0[1,1])
    -1/sqrt(n)*sqrt(f+Tssq)*sqrt(c)*sqrt(s21);
upp=xb[1,2]-ss[1,2]*inv(ss[1,1])*(xb[1,1]-mu0[1,1])
    +1/sqrt(n)*sqrt(f+Tssq)*sqrt(c)*sqrt(s21);
print  low upp;
quit;
          F0             FA
   12.030949      5.3176551
       F0 > Fa:  reject
          LOW           UPP
   (52.693154      63.37719)