[R] Maximization of quadratic forms

Russell Shinohara rshinoha at jhsph.edu
Tue May 18 20:37:06 CEST 2010

Dear R Help,

I am trying to fit a nonlinear model for a mean function $\mu(Data_i, 
\beta)$ for a fixed covariance matrix where $\beta$ and $\mu$ are low- 
dimensional. More specifically, for fixed variance-covariance matrices  
$\Sigma_{z=0}$ and $\Sigma_{z=1}$ (according to a binary covariate $Z 
$), I am trying to minimize:

$\sum_{i=1^n} (Y_i-\mu_(Data_i,\beta))' \Sigma_{z=z_i}^{-1} (Y_i- 

in terms of the parameter $\beta$. Is there a way to do this in R in a  
more stable and efficient fashion than just using a general  
optimization function such as optim? I have tried to use gnls, but I  
was unsuccessful in specifying different values of the covariance  
matrix according to the covariate $Z$.

Thank you very much for your help,
Taki Shinohara


Russell Shinohara, MSc
PhD Candidate and NIH Fellow
Department of Biostatistics
Bloomberg School of Public Health
The Johns Hopkins University
615 N. Wolfe St., Suite E3033
Baltimore, MD 21205
tel: (203) 499-8480

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