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I have the following equation I'd need to solve for η:

equation

where the parameter θ is unknown (the general problem is to estimate it), and the vector h depends on that parameter, and a vector of known values y.

What ideally I would like to get is the vector η=η(θ) as a function of the parameter θ so that I can easily use it later.

Martin Evans
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Ayeron
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    If you want a symbolic solution, that will be impossible or very difficult. Write the right hand side of your equation as a function of `theta` and a vector `eta`. And use a solver for systems of nonlinear equations such as `nleqslv` or `BB`. And you will get numerical solutions if your system has a solution. – Bhas Apr 13 '17 at 08:34
  • a priori the system does have a solution for eta, which is also unique. – Ayeron Apr 13 '17 at 08:36
  • Hoewever the key point is that I need to later use a maximization on another function which depends on eta in order to obtain estimates for theta. – Ayeron Apr 13 '17 at 08:39
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    To me it is not clear, what you are asking: All I read sounds like numerical solution of an equation. Then please provide data if you need further help. If you also want to maximize, you have to specify what you want to maximize and which constraints you have (if at all). – Christoph Apr 13 '17 at 08:51
  • So eta is an n long vector and you wish to estimate eta and theta? Then you have n+1 parameters you need to estimate. That seems like quite a lot. – Therkel Apr 13 '17 at 08:51
  • Thank you all for taking your time. For the full question please go [here](http://math.stackexchange.com/questions/2231338/r-implementation-of-the-maximum-empirical-likelihood-estimation-for-l%C3%A9vy-process), as the whole problem is better explained. In this post I just tried to focus on the part that I am stuck, but yes sorry, it lacks information. – Ayeron Apr 13 '17 at 08:56

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