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My question is general type.Suppose we calculate confidence interval for parameters that are supposed to come from nonlinear model like multivariate nonlinear regression model.I have to calculate Fisher information matrix or Hessian matrix in order to find Covariance matrix that will be subsequently used in construction of confidence intervals.

My question is how we can validate that we have correctly calculated the required interval. In linear case we can validate by coverage probability etc but in nonlinear case how we check the adequacy of calculated interval.

Anyone can help me to find the method or point out any article related .

Thanking you anticipation.

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    $\begingroup$ Instead of calculating covariance matrix, why don't you bootstrap your sample space and re-estimate the parameters for each sample set. Then you can build the confidence interval on the estimated parameter $\endgroup$ – adam Dec 24 '14 at 10:07
  • $\begingroup$ Dear Adam thanks for your suggestions but can you tell me that" bootstrapping is adequate technique in case of many parameters which we need to estimate? $\endgroup$ – zahid khan Dec 29 '14 at 7:08

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