Calculation of parameter confidence intervals

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Calculation of parameter confidence intervals

Charles Ll
Dear all,

I asked the following question in the Julia-Opt mailing list, but was advised to ask for some help here.

I am trying to estimate the confidence intervals of parameters that have been estimated using the JuMP optimisation framework and the Ipopt solver.

For now, I've used parametric and non-parametric bootstrapping, resampling my dataset with a given PDF for the y values in the first case or just resampling my dataset with replacement in the second case.

However, for one of my problems, it takes too much time: I have approximately 50 different large datasets to fit with the same procedure, such that bootstrapping starts to consume too much time, and hence, becomes non-realistic to perform.

I would like to have another "quicker" but robust way to get the confidence interval for my parameters, and I was wondering if anybody has an idea for implementing such function?

From the LsqFit.jl package, I was thinking about writing something like:

    r = y - y_calc # the residuals

    dof = length(r) - length(parameters) # the degrees of freedom

    mse = sumabs2(r)/dof    # mean square error is: standard sum square error / degrees of freedom

    Q,R = qr(J) # compute the covariance matrix from the QR decomposition



Thanks in advance!

Best,
Charles LL.

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