If (X, Y) is an observation with distribution function F(x-heta,y), sigma^{2}={m var}(X), ho={m corr}(X,Y) and I is the Fisher information on heta in (X,Y), then Ige {sigma^{2}(1-ho^{2})}^{-1}. The equality sign holds under conditions closely related to the conditions for linearity of the Pitman estimator of heta from a sample from F(x-heta,y). The results are extensions of earlier results for the case when only the informative component X is observed.
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