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I am estimating parameter $\beta$ as:

\begin{align} \hat \beta &= \mathop{\mathrm{arg\,max}}_\beta \;\; l(\beta;X,y) - \frac{\lambda}{2}\left(\tilde y-g(\beta,\tilde X)\right)^\prime C^\prime C\left(\tilde y-g(\beta,\tilde X)\right)\\ &s.t.\\ & \;\;\;\;\; A\beta\leq 0\\ &where\\ & \tilde y = (y^\prime,y^{\ast\,\prime})^\prime\\ &\tilde X = (X^\prime,X^{\ast\,\prime})^\prime\\ & g(p,Q) = \exp(Qp) \end{align}

How should I go about estimating the confidence limits on $\hat \beta$ theoretically?

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  • $\begingroup$ $ l(\beta;X,y) = ?$ $\endgroup$ – user158565 Dec 7 '18 at 20:27
  • $\begingroup$ Most software would supply an in-buildt method for getting a standard error e.g. using the delta-method. $\endgroup$ – Björn Dec 10 '18 at 10:27
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You can use bootstrap to estimate $\beta$ confidence intervals. Otherwise, you'll need to derive the variance of $\beta$.

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