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I was reading the short intro to nonlinear regression in R by John Fox (Link)

and was wondering where the formula for the variance of the coefficients come from (page 1). The formula for the variance-covariance matrix looks like linear regression but the predictor matrix X in that typical formulation is replaced by the partial derivatives of the function. Can anyone explain this?

Thanks! Brian

B_Miner
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  • It is a standard result of M-estimation theory. The basic idea comes from taylor approximation of the minimizing function. You can look at the derivation in [Wooldridge's book](http://books.google.com/books?id=cdBPOJUP4VsC&lpg=PP1&dq=cross%20sectional%20and%20panel%20data%20wooldridge&hl=fr&pg=PA350#v=onepage&q&f=false), or check out van der Vaart's [Asymptotic Statistics](http://books.google.com/books?id=UEuQEM5RjWgC&lpg=PR1&dq=van%20der%20vaart%20asymptotic%20statistics&hl=fr&pg=PA51#v=onepage&q&f=false). – mpiktas Sep 18 '11 at 08:04
  • Some ideas can be gleaned from this [question](http://stats.stackexchange.com/questions/7308/can-the-empirical-hessian-of-an-m-estimator-be-indefinite) too. – mpiktas Sep 18 '11 at 08:06

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