I am using a minimum chi-square estimator technique to estimate a set of parameters using some sample data (essentially, finding what set of model parameters minimize the difference between observed and expected values, wherein the expected values are calculated through a series of equations). The approach is similar to maximum likelihood estimation, but uses a chi-square objective function instead of a likelihood function.
My question is what is the proper approach for estimating standard errors from this method? With maximum likelihood estimation, one can use the inverse of the Hessian matrix evaluated at the estimated values. Is there a similar technique for minimum chi-square estimation? Can an inverse of the Hessian be used for both? Or is there something else?