OPTIONS LINESIZE=75 PAGESIZE=54 NODATE PAGENO=1;
TITLE 'Ex. 10.1 - A test on SIGMA, the variance-covariance matrix.';
DATA DAT;
 INPUT ID X1-X3;
 CARDS;
 1 1 3 5
 2 2 3 5
 3 1 4 6
 4 1 4 4
 5 3 4 7
 6 2 5 6
DATA XX; SET DAT; DROP ID;
PROC IML;
 RESET NOLOG;
 USE XX;  READ ALL INTO X;
 PRINT "The Data Matrix is" X;
N=NROW(X);  P=NCOL(X);
 XBAR = X(|+,|)`/N;
PRINT, "XBAR = " XBAR;
SUMSQ=X`*X-(XBAR*XBAR`)#N;
S=SUMSQ/(N-1);
PRINT , "The Variance-Covariance Matrix is " S;
NU=N-1;
W=NU#S;
SIG0 = {2 1 0, 1 2 0, 0 0 1};
Q=INV(SIG0)*W;
LAM_STAR = (EXP(1)/NU)##(P#NU/2)#(DET(Q))##(NU/2)#EXP(-.5#TRACE(Q));
PRINT, "LAM_STAR = " LAM_STAR;
L = -2#LOG(LAM_STAR);
PRINT, "L = " L;
B2 = P#(2#P#P+3#P-1)/24;
B3 = -P#(P-1)#(P+1)#(P+2)/32;
F=P#(P+1)/2;
A1 = 1-PROBCHI(L,F);
A2 = 1-PROBCHI(L,F+2);
A3 = 1-PROBCHI(L,F+4);
ALPHA = A1+(1/NU)#B2#(A2-A1)
      +(1/(6#NU#NU))#((3#B2#B2-4#B3)#A3-6#B2#B2#A2
      +(3#B2#B2+4#B3)#A1);
PRINT, "ALPHA = ", ALPHA;
QUIT;