Solving estimating equation using R I am working with different types of data and comparing a variety of estimating equation approaches which share a multi-dimensional parameter $\beta$. Given a set of data $\boldsymbol{X}$, is there an easy way to solve for $\beta$ numerically using R code for an estimating equation of the form: $$U(\boldsymbol{X}, \beta) = 0?$$
I am aware of the function uniroot in one-dimension but how can it be extended to say two or three dimensions?

Without knowing more about your function it is difficult to offer an optimal solution.  However, one approach is to use a general nonlinear optimisation routine to minimise the quantity:
$$L(\beta) \equiv U(\mathbf{X}, \beta)^2.$$
You can use the nlm function in R to undertake nonlinear minimisation of this objective function, including in cases with a vector parameter.  This function also allows you to specify a relevant gradient vector and Hessian matrix if you have analytic results for these (of you can leave them out and R will estimate them numerically).  I often use this method when dealing with cases like this in R and it usually works quite well.  For best performance I recommend using appropriate parameter transforms (if needed) to ensure that you are doing unconstrained optimisation with the nlm function.
