Inadmissibility results for the best invariant estimator of two coordinates of a location vector

Let X=(X1,X2,X3) be a random vector with density f(x..), where .=(.1,.2,.3) is unknown. It is desired to estimate (.1,.2) using an estimator (.1(X),.2(X)), and under a loss function L(.1..1,.2..2). (Note that .3 is a nuisance parameter.) Under certain conditions on f and L, it is shown that the best invariant estimator of (.1,.2) is inadmissible.