Standard Errors for Numerical Optimization using Chi-Square Objective Function 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?

There are various Chi-square minimization methods described in the literature.
All of them boil down to minimizing a sum (or average) of normalized squared residuals (or Chi-square distances).
The normalization constant is usually the predicted value or an average of the predicted value and the observed value.
Provided the data generating process satisfies some mild hypotheses (to be checked), all of these estimators are M-estimators, hence extremum estimators.
Extremum estimators are asymptotically normal and their asymptotic covariance matrix is easy to compute (see, the popular Econometrics book by Fumio Hayashi). The asymptotic covariance can be used to compute standard errors.
