I am doing a nonlinear least squares estimation on a function of 14 variables (meaning that, to estimate ##y=f(x)##, I minimize ##\Sigma_i(y_i-(\hat x_i))^2## ). I do this using the quasi-Newton algorithm in MATLAB. This also gives the Hessian (matrix of second derivatives) at the minimizing point. My point estimates all seem reasonable, but the Hessian does not:(adsbygoogle = window.adsbygoogle || []).push({});

Every value in row ##5## and in column ##5## is zero, except for the entry at (##5, 5##), which is 1. Several of the other entries are also zero.

To find standard errors, you invert the Hessian and take the square root of the diagonals. When I do this, all of the estimates are near 1, and 4 of them are exactly 1.

I went and looked back at the function, and I couldn't see anything blatantly wrong. When I change the value of the 5th parameter, the value of the function changes (as it should); that is pretty much the end of my troubleshooting ability. I don't think the function is badly scaled; all of the parameters are between -2 and 4.

The last thing I should mention is that I had MATLAB calculate the eigenvalues of the Hessian. The first 13 of them were approximately zero, and the last one was 170,000.

Any idea what's going on here? I've calculated the Hessians for very similar functions and not had this issue.

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# I Hessian of least squares estimate behaving strangely

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