The document proposes a new  entropy- based approach for estimating parameters of non linear and complex models, i.e.  those which no transformation renders linear in parameters. Presently, for estimating such class of functions, various iterative technics like the Gauss-Newton algorithm are applied and completed by least square methods approaches. Due to conceptual nature of such methods, definitely estimated functions are different to the original non linear one and estimated values of parameters are in most of cases far from the true values.
The proposed approach, being related to statistical theory of information, is very different from those so far applied for that class of functions. To apply the approach, we select a stochastic non homogeneous constant elasticity of substitution (CES) for aggregated production function of 27 EU countries which we estimate maximizing non extensive entropy function under consistency  restrictions related to the CES model plus regular normality conditions.The procedure might be seen as an attempt to generalize recent works(ex. Golan, al. 1996) on entropy econometrics in the case of ergodic systems, related to Gibbs-Shannon maximum entropy principle. Since this non linear CES estimated model contains  four parameters in  one equation and statistical observations are limited to twelve years, we have to deal with an inverse problem and statistical distribution law of data generating system is unknown. Because of above reason, our approach moves away from normal Gaussian hypothesis to more general Levy instable time (or space) processes characterized by long memory, complex correlation and by convergence, in relative long range, to  attraction basin of central theorem limit. In such a case, fractal properties may eventually exist and the q non extensive parameter could give us useful information. Thus, as already suggested, we will propose to solve for a stochastic inverse problem through the generalized minimum entropy divergence  under the CES model and other normalization factor restrictions. 
At the end, inferential confidence interval for parameters is proposed. Output parameters from entropy represent the long-run state of the system in equilibrium, and so, their interpretation is slightly different from the “ceteris per ibis” interpretation of classical econometrical modeling. The approach seems to produce very efficient parameters in comparison to those obtained from classical iterative non-linear method which will be presented too.

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