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bility literature. This appears to be the first use of these developments to address an open methodological problem. Our simulation studies indicate that our asymptotic results are meaningful in finite samples, and that in specific examples for which other methods exist, our methods generally perform at least as well as these established, tailor-made methods. Of course, the great appeal of our proposal is that it applies to a much wider class of problems. 

We conclude with several possible extensions of our method that may increase further its applicability and appeal. 

1. Although this condition is satisfied in all but one of our examples, requiring R and S to be in S can be somewhat restrictive. Nevertheless, it appears that this condition may be weakened by instead requiring membership to S $^{∗}$, the class of all parameters T for which there exist some M < ∞ and elements T $^{1}$,T $^{2}$,...,T M in S such that T = ∑ M m $_{=1}$T $^{m}$. 

While the results in our paper can be established in a similar manner for functions in this generalized class, the expressions for the involved gradients are quite a bit more complicated. Specifically, we find that, for T,U ∈ S ∗ with T = ∑ M m $_{=1}$T m and U = ∑ L ℓ $_{=1}$U $^{ℓ}$, the quantity ΓTU P ( o$_{1}$,o$_{2}$ ) equals 

<img src='content_image/305679.jpg'>

In particular, we note the need for conditional expectations with respect to X R m and X S m in the definition of Γ, which could render the implementation of our method more difficult. While we believe this extension is promising, its practicality remains to be 

