Hyves, describes the influence of the pjrarameters on the ob- 
servations, i.e. model errors. 
For two multidimensional alternative hypotheses we obtain the 
test statistics for the known and unknown variance factor res- 
pectively: 
  
  
  
  
  
  
  
  
  
I; = 2 i / of = 1'8i1 ^ x'*( Pi: ¥ ) i = 1,2 (3) 
and 
- Q5. / p; 
T: = 2,1 1 wf! ( P4 ,n-u-pi; M ) } = 1,2 (4) 
Hi / (n-u-pi) : 
where Q = v'Py =1PQ,,P] , (5) 
9 s y'PH. i (Pss) 1ln ;Pv ’ (6) 
fte UT (7) 
i = ( PQyyPH; (Pss); 1H? PQyP ) 7 o . (8) 
s HiPQvyPH y . (9) 
Moreover, the residuals y and corresonding cofactor matrix 
Q,, here are obtained from the original model (1) using the 
Least Square estimation: 
Yan Gul (10) 
and 1 
Op =P1- A(A'PA)FUA (11) 
The noncentrality parameter 
2 
a - ( VS: (Pss); vs, ) / Jo (12) 
depends on the geometry (Pas/ii and on the true values 
fv 
VS; = Si Vi with |s,|= t. 
Having onedimensional alternative hypotheses one obtains the 
statistic of data snooping from Eq.(3) and the statistic t 
n-u-1 
of Student-test ( Heck,1981; Fórstner,1980 ) from Eq. (4). 
2.2 Correlations between two test Statistics 
The correlation coefficient between 1w0 x -distribeted test 
statistics ( under Ho ) T, and T, is (see Li, 1985) 
1 1 _ - 
p etUm, ) 4 
T.T, == FR 2218 (13) 
- 190 -