Fuller <see footnote 4) begins with the simple 

 estimator 



O = (*') ' A 



(10) 



with the restriction that the event |<f>l =0 must be 

 impossible. The asymptotic variance-covariance 

 matrix of 6, S ,•, , is given by 



v,^ =(*')-' a, + Siotl'' 



0,2^n(l-<^n) 



111) 



FISHERY BULLETIN: VOL 77, NO 2 



and i^ is defined by Equation (6l 



We remark that variation in estimates of O 

 arises additively from two sources: 1) sampling 

 variation in estimation of the assignment compo- 

 sition of the mixture which is represented by S \; 

 and 2) sampling variation in estimation of the 

 probability of assignment matrix 4^ which is rep- 

 resented by i,,,,|- The diagonal elements of the 1,, 

 are the variances of the elements of (i; the square 

 roots of these are the standard errors. 



where -,i 



S,~4>i24>ii 



Oi'^4>iK4>n 



0, <>i\0,2 



fli20,2(l-0,2) 



Oi'^<t>,K<>i2 





0,2 0,,. (1-0,^,) 



I ' ;■ 



Bias in estimation of (* is approximately given 



by 



B ^(<f) ' GO, 



(12) 



where 



G 



0" 0,1 (1-01 1) 



0^^ 0,2(1-012) 



0'^'l01K(l-01K> 



/.•?I 'l- 



/.•^2 '1- 



h^zK '1- 



12, 



^''■'01101/,. 0'^02l(l-021 



0'''^02102/.- 



I;. 



fc^l 



22, 



0''''0120W,- 0^^022(1-022) 



0''"^02202/.- 



/.■^2 



'01K01;. 0''''02k(1-02k) 



0''^02K02/,- 



/■,, 



/oq£K '2- 



'■• K . 



0"\'>Ki(l-0Ki) 0"''0ki0k;,- 



h 



0^'^'0K2(1-0K2) 



0^'^0KK(l-0K-h-) 



;,-^i 



/.•:^2 



0, 



'■"''' 0K 2 0K/,- 



0''''''0K-K0Kfc 



kz^K 



390 



