A recursive relationship for estimating b results when equations (4) , (5) , and 

 (6) are combined in the following manner: 



b = [(X*'X*) + mx* x*']" 1 [(X'W _1 Y) + my. y fw ] 

 n L n-l n n 1 L n-l n J n n J 



* «, (X*'X*) _1 mx*x*' (X^X*) -1 , I 



1 + w?x* 1 fX X ) .x 



(X'W"^) -1 mx (p -P) 

 = b + n-i n n_ (?) 



n_1 1 + mx '(X'W^X)" 1 x /w 



n n- inn 



Iteration continues until the change in regression coefficients following two suc- 

 cessive passes through the data satisfies the convergence criteria 



where 



6 . = change in ith regression coefficient following successive passes through the 

 data. 



b . = ith regression coefficient 

 n = convergence criteria 



t = small number to handle case where approaches 0. 



Applying equation (7) is similar to adding m identical observations to the solu- 

 tion between successive estimations of the set of parameters. Adding an observation 

 with a large relative weight frequently drives the solution so far that the computer 

 cannot distinguish the resulting estimate of P n from either or 1 , which will termi- 

 nate the iteration abnormally. 



The computational difficulty just discussed has been minimized by setting a limit 

 for the sum of successive weights. The effect of adding each weighted observation to 

 the solution is accumulated. However, the parameter estimates used in the iterative 

 estimation procedure are updated only when the sum of successive weights exceeds the 

 set limit. The same procedures may be used to handle similar problems that arise when 

 data sorting results in runs of O's or l's. 



9 



